Question

[( a+b)²-(b-a)²-ab]²


OBS: a resposta dá 9a²b²

Answer 1

Resposta:

$\boxed{\mathtt{9a^2b^2}}$

Explicação passo-a-passo:

$\\ \displaystyle \mathsf{\left [ (a + b)^2 - (b - a)^2 - ab \right ]^2 =} \\\\ \mathsf{\left [ (b + a)^2 - (b - a)^2 - ab \right ]^2 =} \\\\ \mathsf{\left \{ \left [ (b + a) + (b - a) \right ] \cdot \left [ (b + a) - (b - a) \right ] - ab \right \}^2 =} \\\\ \mathsf{\left [ (b + a + b - a) \cdot (b + a - b + a) - ab \right ]^2 =} \\\\ \mathsf{\left [ (2b) \cdot (2a) - ab \right ]^2 =} \\\\ \mathsf{(4ab - ab)^2 =} \\\\ \mathsf{(3ab)^2 =} \\\\ \boxed{\boxed{\mathsf{9a^2b^2}}}$

Observação: $\displaystyle \boxed{\mathtt{x^2 - y^2 = (x + y) \cdot (x - y)}}$