Question

Fatore as diferenças de dois quadrados a seguir

a) x^2- 4
b) a^2-36
c)y^2-1
d)25x^2-4
e)1/100a^2-1/49
f)x^2y^2-1/9

Me ajudem​

Answer 1

Resposta:

Explicação passo-a-passo:

a) x²-4 = (x+2).(x-2)

b) a² 36 (a+6). (a-6)

c) y²-1 = (Y+1). (Y-1)

d) 25x²-4 = (5x+2) (5x-2)

e)  (a/10 + 1/7).(a/10 - 1/7)

f) ( (xy + 1/3).(xy - 1/3)

   

Answer 2

Explicação passo-a-passo:

a)

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

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

b)

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

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

c)

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

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

d)

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

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

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)

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

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