Question
Simplify the expression
x10−x9
Evaluate
(x2)2(x×1)3(x−1)x2
Multiply the exponents
x2×2(x×1)3(x−1)x2
Any expression multiplied by 1 remains the same
x2×2×x3(x−1)x2
Multiply the numbers
x4×x3(x−1)x2
Multiply the terms with the same base by adding their exponents
x4+3+2(x−1)
Add the numbers
x9(x−1)
Apply the distributive property
x9×x−x9×1
Multiply the terms
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Evaluate
x9×x
Use the product rule an×am=an+m to simplify the expression
x9+1
Add the numbers
x10
x10−x9×1
Solution
x10−x9
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Find the roots
x1=0,x2=1
Evaluate
(x2)2(x×1)3(x−1)(x2)
To find the roots of the expression,set the expression equal to 0
(x2)2(x×1)3(x−1)(x2)=0
Any expression multiplied by 1 remains the same
(x2)2x3(x−1)(x2)=0
Calculate
(x2)2x3(x−1)x2=0
Evaluate the power
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Evaluate
(x2)2
Transform the expression
x2×2
Multiply the numbers
x4
x4×x3(x−1)x2=0
Multiply
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Multiply the terms
x4×x3(x−1)x2
Multiply the terms with the same base by adding their exponents
x4+3+2(x−1)
Add the numbers
x9(x−1)
x9(x−1)=0
Separate the equation into 2 possible cases
x9=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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