Question

simplifique as expressões algébricas seguintes:

a) (x+y)²+2xy

b) (a-1)²+a (3a+2)​

Answer 1

Explicação passo-a-passo:

a).

$(x + y) {}^{2} + 2xy \\ = ( x + y)( \times + y) + 2xy \\ = x {}^{2} + xy + xy + y {}^{2} + 2xy \\ = x {}^{2} + 2xy + y {}^{2} + 2xy \\ = x {}^{2} + y {}^{2} + 2xy + 2xy \\ = x {}^{2} + y {}^{2} + 4xy$

b).

$(a - 1) {}^{2} + a(3a + 2) \\ = (a - 1)(a - 1) + 3a {}^{2} + 2a \\ = a {}^{2} - 2a + 1 + 3a {}^{2} + 2a \\ = a {}^{2} + 3a {}^{2} - 2a + 2a + 1 \\ = 4a {}^{2} + 0 + 1 \\ = 4a {}^{2} + 1$