Question

fatora corretamente:

A)81ª²-b²
B)4x²-1
C)x²-y²
D)x²y²-16a²b²
E) 1/25-a²/4
F)b²-c²016
G)16x²-9y²
H)1-m²-n²
I)x²-100
J)49h²-81p²


Alguém me ajuda por favor, preciso ainda para hoje.​

Answer 1

Explicação passo-a-passo:

a)

$\sf 81a^2-b^2=(9a)^2-b^2$

$\sf 81a^2-b^2=\red{(9a-b)\cdot(9a+b)}$

b)

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

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

c)

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

d)

$\sf x^2y^2-16a^2b^2=(xy)^2-(4ab)^2$

$\sf x^2y^2-16a^2b^2=\red{(xy-4ab)\cdot(xy+4ab)}$

e)

$\sf \dfrac{1}{25}-\dfrac{a^2}{4}=\Big(\dfrac{1}{5}\Big)^2-\Big(\dfrac{a}{2}\Big)^2$

$\sf \dfrac{1}{25}-\dfrac{a^2}{4}=\red{\Big(\dfrac{1}{5}-\dfrac{a}{2}\Big)\cdot\Big(\dfrac{1}{5}+\dfrac{a}{2}\Big)}$

f)

$\sf b^2c^2-16=(bc)^2-4^2$

$\sf b^2c^2-16=\red{(bc-4)\cdot(bc+4)}$

g)

$\sf 16x^2-9y^2=(4x)^2-(3y)^2$

$\sf 16x^2-9y^2=\red{(4x-3y)\cdot(4x+3y)}$

h)

$\sf 1-m^2n^2=1^2-(mn)^2$

$\sf 1-m^2n^2=\red{(1-mn)\cdot(1+mn)}$

i)

$\sf x^2-100=x^2-10^2$

$\sf x^2-100=\red{(x-10)\cdot(x+10)}$

j)

$\sf 49h^2-81p^2=(7h)^2-(9p)^2$

$\sf 49h^2-81p^2=\red{(7h-9p)\cdot(7h+9p)}$