Suggested Answer
AnswerOption B is correct.64x³ + 27 = (4x + 3) (16x² - 12x + 9)ExplanationWe are told to factorize64x³ + 27To do this, we use the factorization of (x³ + y³) as a guide. First of,(x + y)³ = (x + y) (x + y)² = (x + y) (x² + 2xy + y²)(x + y)³ = x³ + y³ + 3x²y + 3xy²So, we can writex³ + y³ = (x + y)³ - 3x²y - 3xy² = (x + y)³ - 3xy(x + y) = (x + y) [(x + y)² - 3xy]= (x + y) (x² + y² + 2xy - 3xy)= (x + y) (x² - xy + y²)So, comparing (64x³ + 27) with (x³ + y³), we can see that 64x³ = (4x)³27 = (3)³(64x³ + 27) = (4x)³ + 3³x³ + y³ = (x + y) (x² - xy + y²)(4x)³ + 3³ = (4x + 3) [(4x)² - (4x × 3) + 3²]= (4x + 3) (16x² - 12x + 9)Hope this Helps!!!
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