Question

Calcule os seguintes produtos notáveis:

(x³+y²)²

(2m+1\4 n )²

(2x+b³)³

Answer 1

Explicação passo-a-passo:

Produtos notáveis

A)

$\mathsf{{({x}^{3}+{y}^{2})}^{2}}$

$\mathsf{{x}^{6}+2{x}^{3}{y}^{2}+{y}^{4}}$

B)

$\mathsf{ {(2m+\frac {1}{4} n)}^{2}}$

$\mathsf{ 4{m}^{2}+mn+\frac {1}{16}{n}^{2}}$

C)

$\mathsf{ {(2x+{b}^{3})}^{3}}$

$\mathsf{ {(8{x}^{3}+12{x}^{2}{b}^{3}+6{b}^{6}x+{b}^{9}})}$

Answer 2

Oie, Td Bom?!

1.

$= (x {}^{3} + y {}^{2} ) {}^{2}$

$= (x {}^{3} ) {}^{2} + 2x {}^{3} y {}^{2} + (y {}^{2} ) {}^{2}$

$= x {}^{6} + 2x {}^{3} y {}^{2} + y {}^{4}$

2.

$= (2m + \frac{1}{4} n) {}^{2}$

$= (2m) {}^{2} + 2 \: . \: 2m \: . \: \frac{1}{4} n + ( \frac{1}{4} n) {}^{2}$

$= 4m {}^{2} + mn + \frac{1}{16} n {}^{2}$

3.

$= (2x + b {}^{3} ) {}^{3}$

$= (2x) {}^{3} + 3 \: . \: (2x) {}^{2} \: . \: b {}^{3} + 3 \: . \: 2x \: . \: (b {}^{3} ) {}^{2} + (b {}^{3} ) {}^{3}$

$= 8x {}^{3} + 12b {}^{3} x {}^{2} + 6b {}^{6} x + b {}^{9}$

Att. Makaveli1996