For a = x and b = 3, which expression represents a^2 − b^2?

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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

For a = x and b = 3, which expression represents a^2 − b^2?

Explanation:
Difference of squares means you take a^2 and subtract b^2, squaring each part separately. With a = x and b = 3, that becomes x^2 − 9. The other expressions don’t match this form: x^2 + 9 adds the squares, not subtracts; x^2 − 6x + 9 is (x − 3)^2 and expands differently; x^2 − 3x − 3x simplifies to x^2 − 6x, missing the 9. So x^2 − 9 is the correct representation.

Difference of squares means you take a^2 and subtract b^2, squaring each part separately. With a = x and b = 3, that becomes x^2 − 9. The other expressions don’t match this form: x^2 + 9 adds the squares, not subtracts; x^2 − 6x + 9 is (x − 3)^2 and expands differently; x^2 − 3x − 3x simplifies to x^2 − 6x, missing the 9. So x^2 − 9 is the correct representation.

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