If x - y = 8 and xy = 5, what is the value of x³ − y³ + 8(x + y)².
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Correct answer: B
Explanation
x − y = 8
xy = 5
According to the formula:
(x − y)² = x² + y² − 2xy
x³ − y³ = (x − y)(x² + xy + y²)
(x − y)² = 8² = 64
x² + y² − 2xy = 64
x² + y² = 64 + 2(5) = 74
x + y= √(x² + y² + 2xy)
= √(74 + 10)
= √84
x³ − y³= (x − y)(x² + xy + y²)
= 8(74 + 5)
= 8 × 79
= 632
8(x + y)²= 8 × 84= 672
Now
x³ − y³ + 8(x + y)²= 632 + 672= 1304