Question

(х+у)^3-(х-у)^3 (а-2)^3+(а+2)^3

Answer 1

(х+у)^3-(х-у)^3=2y*(3x**2+y**2)

(а-2)^3+(а+2)^3=2a*(12+a**2)

Answer 2

1) (x^3+3*x^2*y+3*x*y^2+y^3) - (x^3-3*x^2*y+3*x*y^2-y^3)
Второй найди

Answer 3

To simplify the given expression $(x + y)^3 - (x - y)^3 + (a - 2)^3 + (a + 2)^3$, you can use the identity for the difference of cubes $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. Applying this identity to both the first and the second terms in the expression, you get:

$$[(x + y) - (x - y)][(x + y)^2 + (x + y)(x - y) + (x - y)^2] + (a - 2)^3 + (a + 2)^3$$

Simplifying further:

$$[2y][(x^2 + 2xy + y^2) + (x^2 - y^2) + (x^2 - 2xy + y^2)] + (a - 2)^3 + (a + 2)^3$$

Now, simplify inside the square brackets:

$$[2y][(3x^2 + 2y^2)] + (a - 2)^3 + (a + 2)^3$$

The expression $(a - 2)^3$ and $(a + 2)^3$ are already in their simplest form.

So, the simplified expression is:

$6xy(x^2 + y^2) + (a - 2)^3 + (a + 2)^3$