Question
Simplify the expression
x7−2x6+x5
Evaluate
x2(x×1)(x−1)2x2
Remove the parentheses
x2×x×1×(x−1)2x2
Rewrite the expression
x2×x(x−1)2x2
Multiply the terms with the same base by adding their exponents
x2+1+2(x−1)2
Add the numbers
x5(x−1)2
Expand the expression
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Evaluate
(x−1)2
Use (a−b)2=a2−2ab+b2 to expand the expression
x2−2x×1+12
Calculate
x2−2x+1
x5(x2−2x+1)
Apply the distributive property
x5×x2−x5×2x+x5×1
Multiply the terms
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Evaluate
x5×x2
Use the product rule an×am=an+m to simplify the expression
x5+2
Add the numbers
x7
x7−x5×2x+x5×1
Multiply the terms
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Evaluate
x5×2x
Use the commutative property to reorder the terms
2x5×x
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
2x6
x7−2x6+x5×1
Solution
x7−2x6+x5
Show Solution

Find the roots
x1=0,x2=1
Evaluate
(x2)(x×1)(x−1)2(x2)
To find the roots of the expression,set the expression equal to 0
(x2)(x×1)(x−1)2(x2)=0
Calculate
x2(x×1)(x−1)2(x2)=0
Any expression multiplied by 1 remains the same
x2×x(x−1)2(x2)=0
Calculate
x2×x(x−1)2x2=0
Multiply
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Multiply the terms
x2×x(x−1)2x2
Multiply the terms with the same base by adding their exponents
x2+1+2(x−1)2
Add the numbers
x5(x−1)2
x5(x−1)2=0
Separate the equation into 2 possible cases
x5=0(x−1)2=0
The only way a power can be 0 is when the base equals 0
x=0(x−1)2=0
Solve the equation
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Evaluate
(x−1)2=0
The only way a power can be 0 is when the base equals 0
x−1=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=1
Solution
x1=0,x2=1
Show Solution
