Question
Simplify the expression
9p3−27p2+27p−9
Evaluate
9(p−1)(p−1)2
Multiply the terms with the same base by adding their exponents
9(p−1)1+2
Add the numbers
9(p−1)3
Expand the expression
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Evaluate
(p−1)3
Use (a−b)3=a3−3a2b+3ab2−b3 to expand the expression
p3−3p2×1+3p×12−13
Calculate
p3−3p2+3p−1
9(p3−3p2+3p−1)
Apply the distributive property
9p3−9×3p2+9×3p−9×1
Multiply the numbers
9p3−27p2+9×3p−9×1
Multiply the numbers
9p3−27p2+27p−9×1
Solution
9p3−27p2+27p−9
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Find the roots
p=1
Evaluate
9(p−1)(p−1)2
To find the roots of the expression,set the expression equal to 0
9(p−1)(p−1)2=0
Multiply
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Multiply the terms
9(p−1)(p−1)2
Multiply the terms with the same base by adding their exponents
9(p−1)1+2
Add the numbers
9(p−1)3
9(p−1)3=0
Rewrite the expression
(p−1)3=0
The only way a power can be 0 is when the base equals 0
p−1=0
Move the constant to the right-hand side and change its sign
p=0+1
Solution
p=1
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