QuestionAugust 27, 2025

Factor the following binomial. 169x^2-121 ([?]x+square )(square x-square )

Factor the following binomial. 169x^2-121 ([?]x+square )(square x-square )
Factor the following binomial.
169x^2-121
([?]x+square )(square x-square )

Solution
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Answer

(13x + 11)(13x - 11) Explanation 1. Identify the form of the binomial The given expression 169x^2 - 121 is a difference of squares, which can be factored using the formula a^2 - b^2 = (a+b)(a-b). 2. Determine the square roots Calculate the square root of each term: \sqrt{169x^2} = 13x and \sqrt{121} = 11. 3. Apply the difference of squares formula Substitute the square roots into the formula: (13x + 11)(13x - 11).

Explanation

1. Identify the form of the binomial<br /> The given expression $169x^2 - 121$ is a difference of squares, which can be factored using the formula $a^2 - b^2 = (a+b)(a-b)$.<br />2. Determine the square roots<br /> Calculate the square root of each term: $\sqrt{169x^2} = 13x$ and $\sqrt{121} = 11$.<br />3. Apply the difference of squares formula<br /> Substitute the square roots into the formula: $(13x + 11)(13x - 11)$.
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