Question

(a+b)^3+(a-b)^3 упростить выражение

Answer 1

(а+b)^3+(a-b)^3

a^3+3a^2b+3ab^2+b^3+a^3-3a^2b+3ab^2-b^3

2a^3+6ab^2

Answer 2

To simplify the expression (a+b)^3 + (a-b)^3, we can use the algebraic identity for the sum of cubes:

a^3 + b^3 = (a + b)(a^2 - ab + b^2).

Let's apply this identity to our expression:

(a+b)^3 + (a-b)^3

Using the identity for each term:

= [(a + b)^2 - (a)(b) + (b)^2] + [(a - b)^2 + (a)(b) + (b)^2]

Now, let's further expand the squares:

= [(a^2 + 2ab + b^2) - ab + b^2] + [(a^2 - 2ab + b^2) + ab + b^2]

Next, combine like terms within each bracket:

= a^2 + 2ab + b^2 - ab + b^2 + a^2 - 2ab + b^2 + ab + b^2

Now, simplify by combining like terms:

= (a^2 + a^2) + (2ab - 2ab) + (b^2 + b^2 + b^2) + (-ab + ab)

= 2a^2 + 3b^2

So, the simplified expression is 2a^2 + 3b^2.