Question
Simplify the expression
a3−a2−a+1
Evaluate
(a×1×a−1)(a−1)
Multiply the terms
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Evaluate
a×1×a
Rewrite the expression
a×a
Multiply the terms
a2
(a2−1)(a−1)
Apply the distributive property
a2×a−a2×1−a−(−1)
Multiply the terms
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Evaluate
a2×a
Use the product rule an×am=an+m to simplify the expression
a2+1
Add the numbers
a3
a3−a2×1−a−(−1)
Any expression multiplied by 1 remains the same
a3−a2−a−(−1)
Solution
a3−a2−a+1
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Factor the expression
(a−1)2(a+1)
Evaluate
(a×1×a−1)(a−1)
Multiply the terms
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Evaluate
a×1×a
Rewrite the expression
a×a
Multiply the terms
a2
(a2−1)(a−1)
Use a2−b2=(a−b)(a+b) to factor the expression
(a−1)(a+1)(a−1)
Solution
(a−1)2(a+1)
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Find the roots
a1=−1,a2=1
Evaluate
(a×1×a−1)(a−1)
To find the roots of the expression,set the expression equal to 0
(a×1×a−1)(a−1)=0
Multiply the terms
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Multiply the terms
a×1×a
Rewrite the expression
a×a
Multiply the terms
a2
(a2−1)(a−1)=0
Separate the equation into 2 possible cases
a2−1=0a−1=0
Solve the equation
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Evaluate
a2−1=0
Move the constant to the right-hand side and change its sign
a2=0+1
Removing 0 doesn't change the value,so remove it from the expression
a2=1
Take the root of both sides of the equation and remember to use both positive and negative roots
a=±1
Simplify the expression
a=±1
Separate the equation into 2 possible cases
a=1a=−1
a=1a=−1a−1=0
Solve the equation
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Evaluate
a−1=0
Move the constant to the right-hand side and change its sign
a=0+1
Removing 0 doesn't change the value,so remove it from the expression
a=1
a=1a=−1a=1
Find the union
a=1a=−1
Solution
a1=−1,a2=1
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