Question

Simplify : (x + y)3 - (x - y)3​

Answer 1

Answer:

(x+y)³-(x-y)³.

(x+y)³=x³+y³+3xy(x+y).

(x-y)³=x³-y³-3xy(x-y).

(x+y)³-(x-y)³=(x³+y³+3xy(x+y))-(x³-y³-3xy(x-y)).

=x³+y³+3xy(x+y)-x³+y³+3xy(x+y).

=2y³+2(3xy(x+y)).

=2y³+6xy(2x+2y).

=2(y³+3xy(x+y)).

I think this is your answer.

Answer 2

Answer:

Let us consider,

Here, a = x + y and b = x – y

By using the formula,

[a³ – b³ = (a – b) (a² + ab + b²)]

Let us simplify the given expression, we get

(x + y)3 – (x – y)3 = [(x + y) – (x – y)] [(x + y)² + (x + y) (x – y) + (x – y)]

= (x + y – x + y) [(x² + 2xy + y²) + (x² – y²) + (x² – 2xy + y²)]

= 2y(x² + x² + x² + 2xy – 2xy + y² – y² + y²)

= 2y (3x² + y²)

= 6x²y + 2y³