Question

2 Fatore as diferenças de dois quadrados:
a) p² - 9q²=
b) 4f²-25=
c)(a²/4-b²/9)=
d) 0,04- m²=
e) z⁴-1=
f) 25w²-t⁴=

por favor ,preciso para segunda ​

Answer 1

Explicação passo-a-passo:

a)

$\sf p^2-9q^2=p^2-(3q)^2$

$\sf p^2-9q^2=\red{(p+3q)\cdot(p-3q)}$

b)

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

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

c)

$\sf \dfrac{a^2}{4}-\dfrac{b^2}{9}=\left(\dfrac{a}{2}\right)^2-\left(\dfrac{b}{3}\right)^2$

$\sf \dfrac{a^2}{4}-\dfrac{b^2}{9}=\red{\left(\dfrac{a}{2}+\dfrac{b}{3}\right)\cdot\left(\dfrac{a}{2}-\dfrac{b}{3}\right)}$

d)

$\sf 0,04-m^2=(0,2)^2-m^2$

$\sf 0,04-m^2=\red{(0,2+m)\cdot(0,2-m)}$

e)

$\sf z^4-1=(z^2)^2-1^2$

$\sf z^4-1=(z^2+1)\cdot(z^2-1)$

$\sf z^4-1=\red{(z^2+1)\cdot(z-1)\cdot(z+1)}$

f)

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

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