Question
Factor the trinomial completely. \[ x^{2}+13 x y+40 y^{2} \] Select the correct choice below and, if necessary, fill in the answer box A. \( x^{2}+13 x y+40 y^{2}=\square \) B. The trinomial is pnme.
Ask by Rogers Ramos. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x^{2}+13xy+40y^{2} = (x+8y)(x+5y) \)
Solution
Factor the expression \( x^{2}+13x*y+40y^{2} \).
Factor the expression by following steps:
- step0: Factor:
\(x^{2}+13xy+40y^{2}\)
- step1: Rewrite the expression:
\(x^{2}+\left(5+8\right)xy+40y^{2}\)
- step2: Calculate:
\(x^{2}+5xy+8yx+40y^{2}\)
- step3: Rewrite the expression:
\(x\times x+x\times 5y+8yx+8y\times 5y\)
- step4: Factor the expression:
\(x\left(x+5y\right)+8y\left(x+5y\right)\)
- step5: Factor the expression:
\(\left(x+8y\right)\left(x+5y\right)\)
The trinomial \(x^{2}+13xy+40y^{2}\) can be factored completely as \((x+8y)(x+5y)\).
Therefore, the correct choice is:
A. \(x^{2}+13xy+40y^{2}=(x+8y)(x+5y)\)
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Simplify this solution Extra Insights
To factor the trinomial \( x^{2}+13 xy+40 y^{2} \), we need to find two numbers that multiply to \( 40 \) (the constant term) and add to \( 13 \) (the coefficient of \( xy \)). The numbers \( 8 \) and \( 5 \) satisfy this condition since \( 8 \times 5 = 40 \) and \( 8 + 5 = 13 \). Thus, we can factor the trinomial as: \[ x^{2} + 13xy + 40y^{2} = (x + 8y)(x + 5y) \] The correct choice is: A. \( x^{2}+13 xy+40 y^{2}=(x + 8y)(x + 5y) \)
