Factoring with the Binomial Theorem

Question 7 • FL-1202340-Pre-Calculus Honors A

What is the factored form of the binomial expansion 64x3 − 336x2y + 588xy2 − 343y3?

Answer

(4x – 7y)3

(4x + 7y)3

(8x – 7y)2

(8x + 7y)2

Explanation

Use the binomial formula (a − b)³ = a³ − 3a²b + 3ab² − b³. With a = 4x and b = 7y, the terms are 64x³ − 336x²y + 588xy² − 343y³. Therefore, the factored form is (4x − 7y)³, choice A.

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