QuestionAugust 26, 2025

The factors of x^2-8xy+15y^2 are A (x-15y)(x-y) B (x+15y)(x+y) (x+5y)(x+3y) D (x-5y)(x-3y)

The factors of x^2-8xy+15y^2 are A (x-15y)(x-y) B (x+15y)(x+y) (x+5y)(x+3y) D (x-5y)(x-3y)
The factors of x^2-8xy+15y^2 are A (x-15y)(x-y) B (x+15y)(x+y) (x+5y)(x+3y) D (x-5y)(x-3y)

Solution
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Answer

(x-5y)(x-3y) Explanation 1. Identify the quadratic form The expression x^2 - 8xy + 15y^2 is a quadratic trinomial in the form ax^2 + bxy + cy^2. 2. Find two numbers that multiply to ac and add to b Here, a = 1, b = -8, and c = 15. We need two numbers that multiply to 1 \cdot 15 = 15 and add to -8. These numbers are -5 and -3. 3. Factor using these numbers Rewrite the middle term: x^2 - 5xy - 3xy + 15y^2. Group terms: (x^2 - 5xy) + (-3xy + 15y^2). Factor each group: x(x - 5y) - 3y(x - 5y). 4. Factor out the common binomial Combine: (x - 5y)(x - 3y).

Explanation

1. Identify the quadratic form<br /> The expression $x^2 - 8xy + 15y^2$ is a quadratic trinomial in the form $ax^2 + bxy + cy^2$.<br /><br />2. Find two numbers that multiply to $ac$ and add to $b$<br /> Here, $a = 1$, $b = -8$, and $c = 15$. We need two numbers that multiply to $1 \cdot 15 = 15$ and add to $-8$. These numbers are $-5$ and $-3$.<br /><br />3. Factor using these numbers<br /> Rewrite the middle term: $x^2 - 5xy - 3xy + 15y^2$.<br /> Group terms: $(x^2 - 5xy) + (-3xy + 15y^2)$.<br /> Factor each group: $x(x - 5y) - 3y(x - 5y)$.<br /><br />4. Factor out the common binomial<br /> Combine: $(x - 5y)(x - 3y)$.
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