SAT Math

Category - Algebra and Functions

What is the value of 729x3 − 64y3, if x = 4 and y = 9?
  1. 0
  2. 2
  3. 9
  4. 23
  5. 32
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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