Question

calcule:

(x - 4)$^{3}$

Answer 1

Resposta:

x³ - 12x² + 48x - 64

Explicação passo-a-passo:

(x - 4)³

(x - 4) • (x - 4)²

(x² - 4x - 4x + 16) • (x - 4)

(x² - 8x + 16) • (x - 4)

x³ - 4x² - 8x² + 32x + 16x - 64

x³ - 12x² + 48x - 64

Answer 2

Resposta:

$\boxed{\mathtt{x^3 - 12x^2 + 48x - 64}}$

Explicação passo-a-passo:

Por Binômio de Newton!

$\displaystyle \mathsf{(a + b)^n = \binom{n}{0} a^{n} \cdot b^{0} + \binom{n}{1} a^{n - 1} \cdot b^{1} + ... + \binom{n}{n - 1} a^{1} \cdot b^{n - 1} + \binom{n}{n} a^{0} \cdot b^n}$

Daí,

$\\ \displaystyle \mathsf{(x - 4)^3 =  \binom{3}{0} x^3 \cdot (- 4)^0 + \binom{3}{1} x^2 \cdot (- 4)^1 + \binom{3}{2} x^1 \cdot (- 4)^2 + \binom{3}{3} x^0 \cdot (- 4)^3} \\\\\\ \mathsf{(x - 4)^3 = \frac{3!}{(3 - 0)!0!} \cdot x^3 \cdot 1 + \frac{3!}{(3 - 1)!1!} \cdot x^2 \cdot (- 4) + \frac{3!}{(3 - 2)!2!} \cdot x^1 \cdot 16 + \frac{3!}{(3 - 3)!3!} \cdot 1 \cdot (- 64)} \\\\\\ \mathsf{(x - 4)^3 = \frac{3!}{3!1} \cdot x^3 + \frac{3 \cdot 2!}{2!1} \cdot (- 4x^2) + \frac{3 \cdot 2!}{1 \cdot 2!} \cdot 16x + \frac{3!}{1 \cdot 3!} \cdot (- 64)} \\\\\\ \boxed{\boxed{\mathsf{(x - 4)^3 = x^3 - 12x^2 + 48x - 64}}}$