Question
Simplify the expression
3x3−18x2+36x−24
Evaluate
(x−2)2×3(x−2)
Multiply the terms with the same base by adding their exponents
(x−2)2+1×3
Add the numbers
(x−2)3×3
Use the commutative property to reorder the terms
3(x−2)3
Expand the expression
More Steps

Evaluate
(x−2)3
Use (a−b)3=a3−3a2b+3ab2−b3 to expand the expression
x3−3x2×2+3x×22−23
Calculate
x3−6x2+12x−8
3(x3−6x2+12x−8)
Apply the distributive property
3x3−3×6x2+3×12x−3×8
Multiply the numbers
3x3−18x2+3×12x−3×8
Multiply the numbers
3x3−18x2+36x−3×8
Solution
3x3−18x2+36x−24
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Find the roots
x=2
Evaluate
(x−2)2×3(x−2)
To find the roots of the expression,set the expression equal to 0
(x−2)2×3(x−2)=0
Multiply
More Steps

Multiply the terms
(x−2)2×3(x−2)
Multiply the terms with the same base by adding their exponents
(x−2)2+1×3
Add the numbers
(x−2)3×3
Use the commutative property to reorder the terms
3(x−2)3
3(x−2)3=0
Rewrite the expression
(x−2)3=0
The only way a power can be 0 is when the base equals 0
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Solution
x=2
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