Question

1) Resolva os produtos notáveis abaixo:
a) (x+4)³
b) (b - 2)³

Answer 1

${\bf \rm \large \: A) \: (x \: + \: 4)³}$

${ \bf \rm \large \: x {}^{3} \: + 3x {}^{2} \: \times 4 \: + 3x \times 4 {}^{2} + 4 {}^{3} }$

$\bf \rm \large \: x {}^{3} \: + 12x {}^{2} \: + 3x \times 4 {}^{2} + 4 {}^{3}$

${\bf \rm \large \: x {}^{3} \: + 12x {}^{2} \: + 3x \times 16 + 4 {}^{3} }$

${\bf \rm \large \: x {}^{3} \: + 12x {}^{2} \: + 3x \times 16 + 64 }$

${ \rm \bf \large \: \color{red} \boxed{\boxed{\boxed{x {}^{3} \: + 12x {}^{2} \: + 48x \: + 64}}}}$

$B) \: (b \: - \: 2)³$

$\bf \rm \large \: b {}^{3} - 3b {}^{2} \times 2 \: + 3b \times 2 {}^{2} - 2 {}^{3}$

$\bf \rm \large \: b {}^{3} - 6b {}^{2} + 3b \: \times 2 {}^{2} - 2 {}^{3}$

$\bf \rm \large \: b {}^{3} - 6b {}^{2} \: + 3b\times 4 \: - 2 {}^{3}$

$\bf \rm \large \: b {}^{3} - 6b {}^{2} \: + 3b \times 4 - 8$

$\bf \rm \large \: \color{red}\boxed{ \boxed{ \boxed{b {}^{3} - 6b {}^{2} \: + 12b - 8}}}$