Question

If x - y = 4 and xy = 21 then x³ - y³ = _____

314
316
318
320

Answer 1

Step-by-step explanation:

x + y = 12

Raise both sides to the 3rd power (cube both sides)

(x + y)³ = 12³

(x + y)(x + y)(x + y) = 1728

(x + y)(x² + 2xy + y²) = 1728

x³ + 2x²y + xy² + x²y +2xy² + y³ = 1728

x³ + 3x²y + 3xy² + y³ = 1728

Factor 3xy out of the two middle terms:

x³ + 3xy(x + y) + y³ = 1728

We substitute 27 for xy and 12 for x + y

x³ + 3(27)(12) + y³ = 1728

x³ + 972 + y³ = 1728

x³ + y³ = 756

Answer 2

Answer:

316

Step-by-step explanation:

please see the solution in the picture