Question

Simplify (x + y)3

- (x - y)3

- 6y(x + y) (x - y)​

Answer 1

Answer:

3x⁴-y⁴-6x²+6y²-2x²y²

Step-by-step explanation:

(x+y)³-(x-y)³-6y(x+y)(x-y)

We know that a³-b³= (a-b)(a²+ab+b²)

=[(x+y)(x-y)][(x+y)²+(x-y)²+(x+y)(x-y)]-6y(x+y)(x-y)

= [(x+y)(x-y)][(x+y)²+(x-y)²+(x+y)(x-y)-6]

=(x²-y²)(x²+y²+2xy+x²+y²-2xy+x²-y²-6)

=(x²-y²)(3x²+y²-6)

=3x⁴+x²y²-6x²-3x²y²-y⁴+6y²

=3x⁴-y⁴-6x²+6y²-2x²y²