Question

simplifique as expressões abaixo, utilizando as regras de produtos notáveis e reduza os termos semelhantes: ​

Answer 1

A) (x + 2)² + (x + 1)²

$\rm \: x {}^{2} + 4x + 4 + (x + 1) {}^{2}$

$\rm \: x {}^{2} + 4x + 4 + x {}^{2} + 2x + 1$

$\rm \: 2x {}^{2} + 4x + 4 + 2x + 1$

$\rm \: 2x {}^{2} + 6x + 4 + 1$

$\red{\boxed{ \boxed{ \large \rm \bf \: 2x {}^{2} + 6x + 5}}}$

B) (x -3)² + x (x + 2)² - x³

$\rm \: x {}^{2} - 6x + 9 + x \times (x + 2) {}^{2} - x {}^{3}$

$\rm \: x {}^{2} - 6x + 9 + x \times (x {}^{2} + 4x + 4) - x {}^{3}$

$\rm \: x {}^{2} - 6x + 9 + x {}^{3 } + 4x {}^{2} + 4x - x {}^{3}$

$\rm \: x {}^{2} - 6x + 9 + 4x {}^{2} + 4x$

$\rm 5x {}^{2} - 6x + 9 + 4x$

$\red{\boxed{ \boxed{\large \rm \bf \: 5x {}^{2} - 2x + 9}}}$

C) (a + 3)² - (a - 5)² + 2a (a - 7)

$\rm \: a {}^{2} + 6a + 9 - (a - 5) {}^{2} + 2a \times (a - 7)$

$\rm \: a {}^{2} + 6a + 9 - (a {}^{2} - 10a + 25) + 2a \times (a - 7)$

$\rm \: a {}^{2} + 6a + 9 - (a {}^{2} - 10a + 25) + 2a { }^{2} - 14a$

$\rm \: a {}^{2} + 6a + 9 - a {}^{2} + 10a - 25 + 2a {}^{2} - 14a$

$\rm \: 6a + 9 + 10a - 25 + 2a - 14a$

$\rm \: 2a + 9 - 25 + 2a {}^{2}$

$\rm \: 2a - 16 + 2a {}^{2}$

$\red{ \boxed{\boxed{ \large \rm \bf \: 2a {}^{2} + 2a - 16}}}$

$\green{\large \bf \: Espero \: ter \: ajudado}$