All courses Algebra I · A-SSE.2 56 of 76

Use expression structure to identify useful rewrites, such as difference-of-squares factoring.

Factor a difference of squares

Problem

Factor \(x^{2}-49\) as a difference of squares. Identify both square roots, apply the conjugate identity, and expand the factors to verify the original expression.

Your answer

Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.

A Squares x² and 7²; identity a² − b² = (a − b)(a + b); factorization (x² − 49)(x² + 49); expansion x⁴ − 2401. B Squares x² and 7²; identity a² − b² = (a − b)(a − b); factorization (x − 7)²; expansion x² − 14x + 49. C Squares x² and 7²; identity a² − b² = (a − b)(a + b); factorization (x − 7)(x + 7); expansion x² − 49. D Squares x² and 7²; identity a² + b² = (a + b)(a + b); factorization (x + 7)²; expansion x² + 14x + 49.

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Revisit a weak spot without repeating one problem.

Use additional variants to practice the same idea again while still having to do the mathematics.

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Factor a difference of squares

Take your practice with you.

Revisit a weak spot without repeating one problem.

Hint

Solution walkthrough

Recognize both square terms

Apply the conjugate identity

Write the factorization

Expand to verify

Another way

Common mistake

Solution walkthrough video