Question

(2a+b)^2 - (3b-a)^2
passo a passo plzzzz

Answer 1

Resposta:

(2a+b)^2 - (3b-a)^2

(2a+b) × (2a+b) - (3b-a) × (3b-a)

4a² + 2ab + 2ab + b² - ( 9b² - 3ab - 3ab + a²)

4a² + 2ab + 2ab + b² -9b² + 3ab + 3ab -a²

4a² -a² + 4ab - 8b² + 6 ab

3a² + 10ab -8b²

(a + 4b) × (3a - 2b)

prova: 3a² -2ab + 12ab - 8b²

3a² + 10ab - 8b²

Answer 2

Primeira solução:

$\boxed{(x\pm y)^2=x^2\pm2xy+y^2}$

$(2a+b)^2-(3b-a)^2=\\\\ (2a)^2+2(2a)b+b^2-[(3b)^2-2(3b)a+a^2]=\\\\ 4a^2+4ab+b^2-[a^2-6ab+9b^2]=\\\\ 4a^2+4ab+b^2-a^2+6ab-9b^2=\\\\ \boxed{3a^2+10ab-8b^2}$

Segunda solução:

$\boxed{x^2-y^2=(x+y)(x-y)}$

$(2a+b)^2-(3b-a)^2=\\\\ \big[(2a+b)+(3b-a)\big]\big[(2a+b)-(3b-a)\big]=\\\\ \big[a+4b\big]\big[3a-2b\big]=\\\\ \boxed{3a^2+10ab-8b^2}$