Question

Factor
81x^6-25y^10
Explanation too please

Answer 1

Answer:

$(9x^3+5y^5)(9x^3-5y^5)$

Step-by-step explanation:

$81x^6-25y^{10}$

$81=9^2$

$x^6=x^{3 \cdot 2}=(x^3)^2$

$\implies 81x^6=(9x^3)^2$

$25=5^2$

$y^{10}=y^{5 \cdot 2}=(y^5)^2$

$\implies 25y^{10}=(5y^5)^2$

Therefore,

$81x^6-25y^{10}=(9x^3)^2 -(5y^5)^2$

Apply difference of two squares formula $x^2-y^2=(x+y)(x-y)$:

$\implies (9x^3)^2 -(5y^5)^2=(9x^3+5y^5)(9x^3-5y^5)$