Question

15. Fatore as diferenças de dois quadrados a seguir:

a) x² - 4
b) x² - 36
c) y² - 1
d) 25x²
e) $\frac{1}{100}a^{2}- \frac{1}{49}$
f) x²y² - $\frac{1}{9}$

Answer 1

Explicação passo-a-passo:

a)

$\sf x^2-4=x^2-2^2$

$\sf x^2-4=\red{(x+2)\cdot(x-2)}$

b)

$\sf x^2-36=x^2-6^2$

$\sf x^2-36=\red{(x+6)\cdot(x-6)}$

c)

$\sf y^2-1=y^2-1^2$

$\sf y^2-1=\red{(y+1)\cdot(y-1)}$

d)

$\sf 25x^2-4=(5x)^2-2^2$

$\sf 25x^2-4=\red{(5x+2)\cdot(5x-2)}$

e)

$\sf \dfrac{a^2}{100}-\dfrac{1}{49}=\Big(\dfrac{a}{10}\Big)^2-\Big(\dfrac{1}{7}\Big)^2$

$\sf \dfrac{a^2}{100}-\dfrac{1}{49}=\red{\Big(\dfrac{a}{10}+\dfrac{1}{7}\Big)\cdot\Big(\dfrac{a}{10}-\dfrac{1}{7}\Big)}$

f)

$\sf x^2y^2-\dfrac{1}{9}=(xy)^2-\Big(\dfrac{1}{3}\Big)^2$

$\sf x^2y^2-\dfrac{1}{9}=\red{\Big(xy+\dfrac{1}{3}\Big)\cdot\Big(xy-\dfrac{1}{3}\Big)}$