Which is a valid factorization of x^2 - 9?

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Study for the 8th Grade FAST Mathematics Pre-Algebra Test. Enhance your skills with interactive flashcards and multiple choice questions, each containing hints and explanations to boost your comprehension and readiness for the exam. Get ready to ace your test!

Multiple Choice

Which is a valid factorization of x^2 - 9?

Explanation:
Recognize a difference of squares. An expression like x^2 - 9 is a^2 - b^2 with a = x and b = 3. It factors as (x - 3)(x + 3) because multiplying those gives x^2 + 3x - 3x - 9, which simplifies to x^2 - 9. This is the valid factorization. The other products would introduce extra x terms or constants that don’t cancel to produce x^2 - 9, for example: (x - 9)(x + 1) expands to x^2 - 8x - 9; (x - 3)(x + 9) expands to x^2 + 6x - 27; (x + 3)^2 expands to x^2 + 6x + 9.

Recognize a difference of squares. An expression like x^2 - 9 is a^2 - b^2 with a = x and b = 3. It factors as (x - 3)(x + 3) because multiplying those gives x^2 + 3x - 3x - 9, which simplifies to x^2 - 9. This is the valid factorization. The other products would introduce extra x terms or constants that don’t cancel to produce x^2 - 9, for example: (x - 9)(x + 1) expands to x^2 - 8x - 9; (x - 3)(x + 9) expands to x^2 + 6x - 27; (x + 3)^2 expands to x^2 + 6x + 9.

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