Question

Which of the following is a factor of (x+y)³-(x+y)³

a. x²+y²+2xy
b. x²+y²-xy
c. xy²
d. 3xy

also explain why the part u selected is correct!​

Answer 1

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Answer :

The factor of (x + y)³- (x³ + y³) is 3xy

Step By Step Solution :

→ (x + y)³- (x³ + y³)

→ (x + y) - (x + y)(x² - xy + y²) [Using identity a³ + b³ = (a + b)(a²- ab+ b²)]

→ (x + y)(x² + y² + 2xy - x² + xy - y²)[Using identity, (a + b)² = (a² + b²+ 2ab)]

→ (x + y) (3xy)

→ 3xy

∴ Option d. 3xy is correct!

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Answer 2

(x+y)³= x³+y³+3xy(x+y)

x³+y³+3xy(x+y) - x³-y³

x³ and y³ gets cancelled out, and we are left with

3xy(x+y)

so, we have 3xy as one of our factors.

hope it helps!