Question
Factor completely; simplify if possible. \( 4 x^{3}+32 x^{2}+64 x= \)
Ask by Schofield Donnelly. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression \(4x^3+32x^2+64x\) factors to \(4x(x+4)^2\).
Solution
Factor the expression \( 4x^3+32x^2+64x \).
Factor the expression by following steps:
- step0: Factor:
\(4x^{3}+32x^{2}+64x\)
- step1: Rewrite the expression:
\(4x\times x^{2}+4x\times 8x+4x\times 16\)
- step2: Factor the expression:
\(4x\left(x^{2}+8x+16\right)\)
- step3: Factor the expression:
\(4x\left(x+4\right)^{2}\)
The factored form of the expression \(4x^3+32x^2+64x\) is \(4x(x+4)^2\).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Extra Insights
To factor the expression \( 4x^3 + 32x^2 + 64x \), start by factoring out the greatest common factor, which is \( 4x \): \[ 4x(x^2 + 8x + 16) \] Next, focus on the quadratic expression \( x^2 + 8x + 16 \). This can be factored further because it is a perfect square trinomial: \[ x^2 + 8x + 16 = (x + 4)^2 \] Thus, the fully factored form becomes: \[ 4x(x + 4)^2 \] Now, you have a completely factored expression: \( 4x(x + 4)^2 \).
