QuestionJuly 15, 2025

Factor the binomial completely. x^2-49y^2 Select the correct choice below and, if necessary,fill in the answer box to complete your choice. A. x^2-49y^2=square (Factor completely.) B. The polynomial is prime.

Factor the binomial completely. x^2-49y^2 Select the correct choice below and, if necessary,fill in the answer box to complete your choice. A. x^2-49y^2=square (Factor completely.) B. The polynomial is prime.
Factor the binomial completely.
x^2-49y^2
Select the correct choice below and, if necessary,fill in the answer box to complete your choice.
A. x^2-49y^2=square  (Factor completely.)
B. The polynomial is prime.

Solution
4.2(180 votes)

Answer

x^{2}-49y^{2}=(x-7y)(x+7y) Explanation 1. Recognize the difference of squares The expression x^2 - 49y^2 is a difference of squares, where a^2 - b^2 = (a-b)(a+b). 2. Identify a and b Here, a = x and b = 7y, since (7y)^2 = 49y^2. 3. Apply the difference of squares formula Substitute a and b into the formula: (x - 7y)(x + 7y).

Explanation

1. Recognize the difference of squares<br /> The expression $x^2 - 49y^2$ is a difference of squares, where $a^2 - b^2 = (a-b)(a+b)$.<br />2. Identify $a$ and $b$<br /> Here, $a = x$ and $b = 7y$, since $(7y)^2 = 49y^2$.<br />3. Apply the difference of squares formula<br /> Substitute $a$ and $b$ into the formula: $(x - 7y)(x + 7y)$.
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