Question

A³+b³ if a+b=3ab=2 please help me​

Answer 1

Answer:

$a^3 + b^3 = -4$

Step-by-step explanation:

Given

$a + b = 3ab = 2$

Required

Solve: $a^3 + b^3$

Rewrite the expression as:

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

Factorize

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

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

Rewrite as:

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

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

Factorize

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

Open brackets

$a^3 + b^3 = (a + b)^3 - 3ab(a + b)$

Given that:

$a + b = 3ab = 2$

This means that:

$a + b = 2$ and $3ab = 2$

So, we have:

$a^3 + b^3 = (a + b)^3 - 3ab(a + b)$

$a^3 + b^3 = 2^3 - 3 * 2 * 2$

$a^3 + b^3 = 8 - 12$

$a^3 + b^3 = -4$