Answer: A - The value of the expression is 0. Use x3 − y3 = (x − y)(x2 + xy + y2 )729x3 − 64y3 = (9x)3 − (4y)3 = (9x − 4y)(81x2 + 36xy + 16y2 ) = = (9 × 4 − 4 × 9)(81 × 42 + 36 × 4 × 9 + 16 × 92 ) = = 0 × (81 × 42 + 36 × 4 × 9 + 16 × 92 ) = 0

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SAT Math

Category - Algebra and Functions

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What is the value of 729x³ − 64y³, if x = 4 and y = 9?

Explanation

Answer: A - The value of the expression is 0.

Use x³ − y³ = (x − y)(x² + xy + y² )

729x³ − 64y³ = (9x)³ − (4y)³ = (9x − 4y)(81x² + 36xy + 16y² ) =
= (9 × 4 − 4 × 9)(81 × 4² + 36 × 4 × 9 + 16 × 9² ) =
= 0 × (81 × 4² + 36 × 4 × 9 + 16 × 9² ) = 0

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