Question
Simplify the expression
x6−x5
Evaluate
x3×x2(x−1)
Multiply the terms with the same base by adding their exponents
x3+2(x−1)
Add the numbers
x5(x−1)
Apply the distributive property
x5×x−x5×1
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−x5×1
Solution
x6−x5
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Find the roots
x1=0,x2=1
Evaluate
(x3)(x2)(x−1)
To find the roots of the expression,set the expression equal to 0
(x3)(x2)(x−1)=0
Calculate
x3(x2)(x−1)=0
Calculate
x3×x2(x−1)=0
Multiply
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Multiply the terms
x3×x2(x−1)
Multiply the terms with the same base by adding their exponents
x3+2(x−1)
Add the numbers
x5(x−1)
x5(x−1)=0
Separate the equation into 2 possible cases
x5=0x−1=0
The only way a power can be 0 is when the base equals 0
x=0x−1=0
Solve the equation
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Evaluate
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
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