Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
−31x3+28x2−x5+10x4
Evaluate
(x−4)x2−(x−4)2x2(x−2)
Multiply the terms
x2(x−4)−(x−4)2x2(x−2)
Use the commutative property to reorder the terms
x2(x−4)−x2(x−4)2(x−2)
Expand the expression
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Calculate
x2(x−4)
Apply the distributive property
x2×x−x2×4
Multiply the terms
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Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x3−x2×4
Use the commutative property to reorder the terms
x3−4x2
x3−4x2−x2(x−4)2(x−2)
Expand the expression
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Calculate
−x2(x−4)2(x−2)
Simplify
−x2(x2−8x+16)(x−2)
Simplify
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Evaluate
−x2(x2−8x+16)
Apply the distributive property
−x2×x2−(−x2×8x)−x2×16
Multiply the terms
−x4−(−x2×8x)−x2×16
Multiply the terms
−x4−(−8x3)−x2×16
Use the commutative property to reorder the terms
−x4−(−8x3)−16x2
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+8x3−16x2
(−x4+8x3−16x2)(x−2)
Apply the distributive property
−x4×x−(−x4×2)+8x3×x−8x3×2−16x2×x−(−16x2×2)
Multiply the terms
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Evaluate
x4×x
Use the product rule an×am=an+m to simplify the expression
x4+1
Add the numbers
x5
−x5−(−x4×2)+8x3×x−8x3×2−16x2×x−(−16x2×2)
Use the commutative property to reorder the terms
−x5−(−2x4)+8x3×x−8x3×2−16x2×x−(−16x2×2)
Multiply the terms
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Evaluate
x3×x
Use the product rule an×am=an+m to simplify the expression
x3+1
Add the numbers
x4
−x5−(−2x4)+8x4−8x3×2−16x2×x−(−16x2×2)
Multiply the numbers
−x5−(−2x4)+8x4−16x3−16x2×x−(−16x2×2)
Multiply the terms
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Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
−x5−(−2x4)+8x4−16x3−16x3−(−16x2×2)
Multiply the numbers
−x5−(−2x4)+8x4−16x3−16x3−(−32x2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−x5+2x4+8x4−16x3−16x3+32x2
Add the terms
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Evaluate
2x4+8x4
Collect like terms by calculating the sum or difference of their coefficients
(2+8)x4
Add the numbers
10x4
−x5+10x4−16x3−16x3+32x2
Subtract the terms
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Evaluate
−16x3−16x3
Collect like terms by calculating the sum or difference of their coefficients
(−16−16)x3
Subtract the numbers
−32x3
−x5+10x4−32x3+32x2
x3−4x2−x5+10x4−32x3+32x2
Subtract the terms
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Evaluate
x3−32x3
Collect like terms by calculating the sum or difference of their coefficients
(1−32)x3
Subtract the numbers
−31x3
−31x3−4x2−x5+10x4+32x2
Solution
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Evaluate
−4x2+32x2
Collect like terms by calculating the sum or difference of their coefficients
(−4+32)x2
Add the numbers
28x2
−31x3+28x2−x5+10x4
Show Solution
Factor the expression
x2(x−4)(−7−x2+6x)
Evaluate
(x−4)x2−(x−4)2x2(x−2)
Multiply the terms
x2(x−4)−(x−4)2x2(x−2)
Use the commutative property to reorder the terms
x2(x−4)−x2(x−4)2(x−2)
Rewrite the expression
x2(x−4)+x2(x−4)(−x+4)(x−2)
Factor out x2(x−4) from the expression
x2(x−4)(1+(−x+4)(x−2))
Solution
x2(x−4)(−7−x2+6x)
Show Solution
Find the roots
x1=0,x2=3−2,x3=4,x4=3+2
Alternative Form
x1=0,x2≈1.585786,x3=4,x4≈4.414214
Evaluate
(x−4)(x2)−(x−4)2(x2)(x−2)
To find the roots of the expression,set the expression equal to 0
(x−4)(x2)−(x−4)2(x2)(x−2)=0
Calculate
(x−4)x2−(x−4)2(x2)(x−2)=0
Calculate
(x−4)x2−(x−4)2x2(x−2)=0
Multiply the terms
x2(x−4)−(x−4)2x2(x−2)=0
Use the commutative property to reorder the terms
x2(x−4)−x2(x−4)2(x−2)=0
Calculate
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Evaluate
x2(x−4)−x2(x−4)2(x−2)
Expand the expression
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Calculate
x2(x−4)
Apply the distributive property
x2×x−x2×4
Multiply the terms
x3−x2×4
Use the commutative property to reorder the terms
x3−4x2
x3−4x2−x2(x−4)2(x−2)
Expand the expression
More Steps
Calculate
−x2(x−4)2(x−2)
Simplify
−x2(x2−8x+16)(x−2)
Simplify
(−x4+8x3−16x2)(x−2)
Apply the distributive property
−x4×x−(−x4×2)+8x3×x−8x3×2−16x2×x−(−16x2×2)
Multiply the terms
−x5−(−x4×2)+8x3×x−8x3×2−16x2×x−(−16x2×2)
Use the commutative property to reorder the terms
−x5−(−2x4)+8x3×x−8x3×2−16x2×x−(−16x2×2)
Multiply the terms
−x5−(−2x4)+8x4−8x3×2−16x2×x−(−16x2×2)
Multiply the numbers
−x5−(−2x4)+8x4−16x3−16x2×x−(−16x2×2)
Multiply the terms
−x5−(−2x4)+8x4−16x3−16x3−(−16x2×2)
Multiply the numbers
−x5−(−2x4)+8x4−16x3−16x3−(−32x2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−x5+2x4+8x4−16x3−16x3+32x2
Add the terms
−x5+10x4−16x3−16x3+32x2
Subtract the terms
−x5+10x4−32x3+32x2
x3−4x2−x5+10x4−32x3+32x2
Subtract the terms
More Steps
Evaluate
x3−32x3
Collect like terms by calculating the sum or difference of their coefficients
(1−32)x3
Subtract the numbers
−31x3
−31x3−4x2−x5+10x4+32x2
Add the terms
More Steps
Evaluate
−4x2+32x2
Collect like terms by calculating the sum or difference of their coefficients
(−4+32)x2
Add the numbers
28x2
−31x3+28x2−x5+10x4
−31x3+28x2−x5+10x4=0
Factor the expression
x2(4−x)(7+x2−6x)=0
Separate the equation into 3 possible cases
x2=04−x=07+x2−6x=0
The only way a power can be 0 is when the base equals 0
x=04−x=07+x2−6x=0
Solve the equation
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Evaluate
4−x=0
Move the constant to the right-hand side and change its sign
−x=0−4
Removing 0 doesn't change the value,so remove it from the expression
−x=−4
Change the signs on both sides of the equation
x=4
x=0x=47+x2−6x=0
Solve the equation
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Evaluate
7+x2−6x=0
Rewrite in standard form
x2−6x+7=0
Substitute a=1,b=−6 and c=7 into the quadratic formula x=2a−b±b2−4ac
x=26±(−6)2−4×7
Simplify the expression
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Evaluate
(−6)2−4×7
Multiply the numbers
(−6)2−28
Rewrite the expression
62−28
Evaluate the power
36−28
Subtract the numbers
8
x=26±8
Simplify the radical expression
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Evaluate
8
Write the expression as a product where the root of one of the factors can be evaluated
4×2
Write the number in exponential form with the base of 2
22×2
The root of a product is equal to the product of the roots of each factor
22×2
Reduce the index of the radical and exponent with 2
22
x=26±22
Separate the equation into 2 possible cases
x=26+22x=26−22
Simplify the expression
x=3+2x=26−22
Simplify the expression
x=3+2x=3−2
x=0x=4x=3+2x=3−2
Solution
x1=0,x2=3−2,x3=4,x4=3+2
Alternative Form
x1=0,x2≈1.585786,x3=4,x4≈4.414214
Show Solution