Question
Complete the factoring of the polynomial. \[ 2 x^{2} y^{2}+2 x^{5} y=2 x^{2} y( \]
Ask by Bowers Lindsey. in the United States
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The factored form is \(2x^{2}y(y+x^{3})\).
Solution
Factor the expression \( 2x^2y^2+2x^5y \).
Factor the expression by following steps:
- step0: Factor:
\(2x^{2}y^{2}+2x^{5}y\)
- step1: Rewrite the expression:
\(2x^{2}y\times y+2x^{2}yx^{3}\)
- step2: Factor the expression:
\(2x^{2}y\left(y+x^{3}\right)\)
The factored form of the polynomial \(2x^{2}y^{2}+2x^{5}y\) is \(2x^{2}y(y+x^{3})\).
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Simplify this solution Bonus Knowledge
To complete the factoring of the polynomial \( 2 x^{2} y^{2}+2 x^{5} y \), we continued from the expression you started: \[ 2 x^{2} y( \] Next, we factor out the common terms from the remaining expression inside the parentheses. We observe that the remaining terms are \( y + x^3 \), so we can write: \[ 2 x^{2} y (y + x^{3}) \] Thus, the complete factored form is: \[ 2 x^{2} y (y + x^{3}) \] Now you have the polynomial completely factored!
