Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x5−ex4−x4d+ex3d−x4c+ex3c+x3cd−ex2cd−x4b+ex3b+x3bd−ex2bd+x3bc−ex2bc−x2bcd+exbcd−ax4+eax3+ax3d−eax2d+ax3c−eax2c−ax2cd+eaxcd+abx3−eabx2−abx2d+eabxd−abcx2+eabcx+abcdx−eabcd
Evaluate
(x−a)(x−b)(x−c)(x−d)(x−e)
Multiply the terms
More Steps
Evaluate
(x−a)(x−b)
Apply the distributive property
x×x−xb−ax−(−ab)
Multiply the terms
x2−xb−ax−(−ab)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x2−xb−ax+ab
(x2−xb−ax+ab)(x−c)(x−d)(x−e)
Multiply the terms
More Steps
Evaluate
(x2−xb−ax+ab)(x−c)
Apply the distributive property
x2×x−x2c−xbx−(−xbc)−ax×x−(−axc)+abx−abc
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x3−x2c−xbx−(−xbc)−ax×x−(−axc)+abx−abc
Multiply the terms
x3−x2c−x2b−(−xbc)−ax×x−(−axc)+abx−abc
Multiply the terms
x3−x2c−x2b−(−xbc)−ax2−(−axc)+abx−abc
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x3−x2c−x2b+xbc−ax2+axc+abx−abc
(x3−x2c−x2b+xbc−ax2+axc+abx−abc)(x−d)(x−e)
Multiply the terms
More Steps
Evaluate
(x3−x2c−x2b+xbc−ax2+axc+abx−abc)(x−d)
Apply the distributive property
x3×x−x3d−x2cx−(−x2cd)−x2bx−(−x2bd)+xbcx−xbcd−ax2×x−(−ax2d)+axcx−axcd+abx×x−abxd−abcx−(−abcd)
Multiply the terms
More Steps
Evaluate
x3×x
Use the product rule an×am=an+m to simplify the expression
x3+1
Add the numbers
x4
x4−x3d−x2cx−(−x2cd)−x2bx−(−x2bd)+xbcx−xbcd−ax2×x−(−ax2d)+axcx−axcd+abx×x−abxd−abcx−(−abcd)
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x4−x3d−x3c−(−x2cd)−x2bx−(−x2bd)+xbcx−xbcd−ax2×x−(−ax2d)+axcx−axcd+abx×x−abxd−abcx−(−abcd)
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x4−x3d−x3c−(−x2cd)−x3b−(−x2bd)+xbcx−xbcd−ax2×x−(−ax2d)+axcx−axcd+abx×x−abxd−abcx−(−abcd)
Multiply the terms
x4−x3d−x3c−(−x2cd)−x3b−(−x2bd)+x2bc−xbcd−ax2×x−(−ax2d)+axcx−axcd+abx×x−abxd−abcx−(−abcd)
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x4−x3d−x3c−(−x2cd)−x3b−(−x2bd)+x2bc−xbcd−ax3−(−ax2d)+axcx−axcd+abx×x−abxd−abcx−(−abcd)
Multiply the terms
x4−x3d−x3c−(−x2cd)−x3b−(−x2bd)+x2bc−xbcd−ax3−(−ax2d)+ax2c−axcd+abx×x−abxd−abcx−(−abcd)
Multiply the terms
x4−x3d−x3c−(−x2cd)−x3b−(−x2bd)+x2bc−xbcd−ax3−(−ax2d)+ax2c−axcd+abx2−abxd−abcx−(−abcd)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x4−x3d−x3c+x2cd−x3b+x2bd+x2bc−xbcd−ax3+ax2d+ax2c−axcd+abx2−abxd−abcx+abcd
(x4−x3d−x3c+x2cd−x3b+x2bd+x2bc−xbcd−ax3+ax2d+ax2c−axcd+abx2−abxd−abcx+abcd)(x−e)
Apply the distributive property
x4×x−x4e−x3dx−(−x3de)−x3cx−(−x3ce)+x2cdx−x2cde−x3bx−(−x3be)+x2bdx−x2bde+x2bcx−x2bce−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
More Steps
Evaluate
x4×x
Use the product rule an×am=an+m to simplify the expression
x4+1
Add the numbers
x5
x5−x4e−x3dx−(−x3de)−x3cx−(−x3ce)+x2cdx−x2cde−x3bx−(−x3be)+x2bdx−x2bde+x2bcx−x2bce−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x3dx−(−x3de)−x3cx−(−x3ce)+x2cdx−x2cde−x3bx−(−x3be)+x2bdx−x2bde+x2bcx−x2bce−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
More Steps
Evaluate
x3×x
Use the product rule an×am=an+m to simplify the expression
x3+1
Add the numbers
x4
x5−ex4−x4d−(−x3de)−x3cx−(−x3ce)+x2cdx−x2cde−x3bx−(−x3be)+x2bdx−x2bde+x2bcx−x2bce−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x3cx−(−x3ce)+x2cdx−x2cde−x3bx−(−x3be)+x2bdx−x2bde+x2bcx−x2bce−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
More Steps
Evaluate
x3×x
Use the product rule an×am=an+m to simplify the expression
x3+1
Add the numbers
x4
x5−ex4−x4d−(−ex3d)−x4c−(−x3ce)+x2cdx−x2cde−x3bx−(−x3be)+x2bdx−x2bde+x2bcx−x2bce−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x2cdx−x2cde−x3bx−(−x3be)+x2bdx−x2bde+x2bcx−x2bce−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−x2cde−x3bx−(−x3be)+x2bdx−x2bde+x2bcx−x2bce−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x3bx−(−x3be)+x2bdx−x2bde+x2bcx−x2bce−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
More Steps
Evaluate
x3×x
Use the product rule an×am=an+m to simplify the expression
x3+1
Add the numbers
x4
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−x3be)+x2bdx−x2bde+x2bcx−x2bce−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x2bdx−x2bde+x2bcx−x2bce−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−x2bde+x2bcx−x2bce−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x2bcx−x2bce−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−x2bce−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−xbcdx−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−xbcde)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax3×x−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
More Steps
Evaluate
x3×x
Use the product rule an×am=an+m to simplify the expression
x3+1
Add the numbers
x4
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−ax3e)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−eax3)+ax2dx−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−eax3)+ax3d−ax2de+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−eax3)+ax3d−eax2d+ax2cx−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−eax3)+ax3d−eax2d+ax3c−ax2ce−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−eax3)+ax3d−eax2d+ax3c−eax2c−axcdx−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−eax3)+ax3d−eax2d+ax3c−eax2c−ax2cd−(−axcde)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−eax3)+ax3d−eax2d+ax3c−eax2c−ax2cd−(−eaxcd)+abx2×x−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−eax3)+ax3d−eax2d+ax3c−eax2c−ax2cd−(−eaxcd)+abx3−abx2e−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−eax3)+ax3d−eax2d+ax3c−eax2c−ax2cd−(−eaxcd)+abx3−eabx2−abxdx−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−eax3)+ax3d−eax2d+ax3c−eax2c−ax2cd−(−eaxcd)+abx3−eabx2−abx2d−(−abxde)−abcx×x−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−eax3)+ax3d−eax2d+ax3c−eax2c−ax2cd−(−eaxcd)+abx3−eabx2−abx2d−(−eabxd)−abcx×x−(−abcxe)+abcdx−abcde
Multiply the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−eax3)+ax3d−eax2d+ax3c−eax2c−ax2cd−(−eaxcd)+abx3−eabx2−abx2d−(−eabxd)−abcx2−(−abcxe)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−eax3)+ax3d−eax2d+ax3c−eax2c−ax2cd−(−eaxcd)+abx3−eabx2−abx2d−(−eabxd)−abcx2−(−eabcx)+abcdx−abcde
Use the commutative property to reorder the terms
x5−ex4−x4d−(−ex3d)−x4c−(−ex3c)+x3cd−ex2cd−x4b−(−ex3b)+x3bd−ex2bd+x3bc−ex2bc−x2bcd−(−exbcd)−ax4−(−eax3)+ax3d−eax2d+ax3c−eax2c−ax2cd−(−eaxcd)+abx3−eabx2−abx2d−(−eabxd)−abcx2−(−eabcx)+abcdx−eabcd
Solution
x5−ex4−x4d+ex3d−x4c+ex3c+x3cd−ex2cd−x4b+ex3b+x3bd−ex2bd+x3bc−ex2bc−x2bcd+exbcd−ax4+eax3+ax3d−eax2d+ax3c−eax2c−ax2cd+eaxcd+abx3−eabx2−abx2d+eabxd−abcx2+eabcx+abcdx−eabcd
Show Solution
