Question

fatore as expressões
81 - x⁴

4x² - y²

16x⁴ - 9

36x² - 4y²

16a² - 9x²y²

25x⁴ - y^6

x⁴ - y⁴​

Answer 1

Explicação passo-a-passo:

São diferenças de quadrados

De modo geral:

$\sf a^2-b^2=(a-b)\cdot(a+b)$

a) $\sf 81-x^4$

$\sf =9^2-(x^2)^2$

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

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

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

b) $\sf 4x^2-y^2$

$\sf =(2x)^2-y^2$

$\sf =(2x-y)\cdot(2x+y)$

c) $\sf 16x^4-9$

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

$\sf =(4x^2-3)\cdot(4x^2+3)$

d) $\sf 36x^2-4y^2$

$\sf =(6x)^2-(2y)^2$

$\sf =(6x-2y)\cdot(6x+2y)$

e) $\sf 16a^2-9x^2y^2$

$\sf =(4a)^2-(3xy)^2$

$\sf =(4a-3xy)\cdot(4a+3xy)$

f) $\sf 25x^4-y^6$

$\sf =(5x^2)^2-(y^3)^2$

$\sf =(5x^2-y^3)\cdot(5x^2+y^3)$

g) $\sf x^4-y^4$

$\sf =(x^2)^2-(y^2)^2$

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

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