Question

resolva:
a) (x+⅓)²
b) (x+5)²
c) (x-3)²
d) (x-1/7)²
e) (3-⅓x)²
f) x(x+5)²-(x+3)²
alguém me ajuda

Answer 1

a)

$\left(x + \dfrac{1}{3}\right)^2 = x^2 + 2 \cdot x \cdot \dfrac{1}{3} + \left( \dfrac{1}{3} \right) ^2 \\\\\left(x + \dfrac{1}{3}\right)^2 = x^2 + \dfrac{2}{3}\cdot x + \dfrac{1}{9}$

b)

$(x + 5)^2 = x^2 + 2 \cdot x \cdot 5 + 5^2 \\(x + 5)^2 = x^2 + 10x + 25$

c)

$(x-3)^2 = x^2 - 2\cdot x \cdot 3 + 3^2 \\(x-3)^2 = x^2 - 6x + 9$

d)

$\left(x - \dfrac{1}{7}\right)^2 = x^2 - 2 \cdot x \cdot \dfrac{1}{7} + \left( \dfrac{1}{7} \right) ^2 \\\\\left(x - \dfrac{1}{7}\right)^2 = x^2 - \dfrac{2}{7} \cdot x + \dfrac{1}{49}$

e)

$\left(3 - \dfrac{x}{3}\right)^2 = 3^2 - 2 \cdot 3 \cdot \dfrac{x}{3} + \left( \dfrac{x}{3} \right) ^2 \\\\\left(3 - \dfrac{x}{3}\right)^2 = 9 - 2x + \dfrac{x^2}{9}$

f)

$x(x+5)^2 = x \cdot (x^2 + 10x + 25) \\x(x+5)^2 = x^3 + 10x^2 + 25x \\\\(x+3)^2 = x^2 + 6x + 9 \\\\(x^3 + 10x^2 + 25x) - (x^2 + 6x + 9) \\x^3 + 10x^2 + 25x - x^2 - 6x - 9 \\x^3 + 10x^2 - x^2 + 25x - 6x - 9 \\x^3 + 9x^2 + 19x - 9$