Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x2−5x−x6+5x5
Evaluate
x(x−5)−x5(x−5)
Expand the expression
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Calculate
x(x−5)
Apply the distributive property
x×x−x×5
Multiply the terms
x2−x×5
Use the commutative property to reorder the terms
x2−5x
x2−5x−x5(x−5)
Solution
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Calculate
−x5(x−5)
Apply the distributive property
−x5×x−(−x5×5)
Multiply the terms
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Evaluate
x5×x
Use the product rule an×am=an+m to simplify the expression
x5+1
Add the numbers
x6
−x6−(−x5×5)
Use the commutative property to reorder the terms
−x6−(−5x5)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−x6+5x5
x2−5x−x6+5x5
Show Solution
Factor the expression
x(x−5)(1−x)(1+x)(1+x2)
Evaluate
x(x−5)−(x5)(x−5)
Evaluate
x(x−5)−x5(x−5)
Factor out x(x−5) from the expression
x(x−5)(1−x4)
Factor the expression
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Evaluate
1−x4
Rewrite the expression in exponential form
12−(x2)2
Use a2−b2=(a−b)(a+b) to factor the expression
(1−x2)(1+x2)
x(x−5)(1−x2)(1+x2)
Solution
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Evaluate
1−x2
Rewrite the expression in exponential form
12−x2
Use a2−b2=(a−b)(a+b) to factor the expression
(1−x)(1+x)
x(x−5)(1−x)(1+x)(1+x2)
Show Solution
Find the roots
x1=−i,x2=i,x3=−1,x4=0,x5=1,x6=5
Evaluate
x(x−5)−(x5)(x−5)
To find the roots of the expression,set the expression equal to 0
x(x−5)−(x5)(x−5)=0
Calculate
x(x−5)−x5(x−5)=0
Factor the expression
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Evaluate
x(x−5)−x5(x−5)
Factor out x(x−5) from the expression
x(x−5)(1−x4)
Factor the expression
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Evaluate
1−x4
Rewrite the expression in exponential form
12−(x2)2
Use a2−b2=(a−b)(a+b) to factor the expression
(1−x2)(1+x2)
x(x−5)(1−x2)(1+x2)
Evaluate
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Evaluate
1−x2
Rewrite the expression in exponential form
12−x2
Use a2−b2=(a−b)(a+b) to factor the expression
(1−x)(1+x)
x(x−5)(1−x)(1+x)(1+x2)
x(x−5)(1−x)(1+x)(1+x2)=0
Separate the equation into 5 possible cases
x=0x−5=01−x=01+x=01+x2=0
Solve the equation
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Evaluate
x−5=0
Move the constant to the right-hand side and change its sign
x=0+5
Removing 0 doesn't change the value,so remove it from the expression
x=5
x=0x=51−x=01+x=01+x2=0
Solve the equation
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Evaluate
1−x=0
Move the constant to the right-hand side and change its sign
−x=0−1
Removing 0 doesn't change the value,so remove it from the expression
−x=−1
Change the signs on both sides of the equation
x=1
x=0x=5x=11+x=01+x2=0
Solve the equation
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Evaluate
1+x=0
Move the constant to the right-hand side and change its sign
x=0−1
Removing 0 doesn't change the value,so remove it from the expression
x=−1
x=0x=5x=1x=−11+x2=0
Solve the equation
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Evaluate
1+x2=0
Move the constant to the right-hand side and change its sign
x2=0−1
Removing 0 doesn't change the value,so remove it from the expression
x2=−1
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±−1
Simplify the expression
x=±i
Separate the equation into 2 possible cases
x=ix=−i
x=0x=5x=1x=−1x=ix=−i
Solution
x1=−i,x2=i,x3=−1,x4=0,x5=1,x6=5
Show Solution