Question

125x⁶-81 factoring pls help​

Answer 1

Use Algebraic Identities

Step-by-step explanation:

We can solve the question by using algebraic identity -

$a^2 - b^2 = (a+b)(a-b)$

Also

$a^3 - b^3 = (a-b)(a^2 + ab + b^2)$

Let us write $A = A(x,y) = 125x^6 - 81$

Now as per the question -

$125x^6 = (5x^2)^3 \\and\\ 8y^6 = (2y^2)^3$

hence, $A = A_1A_2$ = $(5x^2 - 2y^2)(25x^4 + 10x^2y^2 + 4y^4)$

where $P_1$ is a difference of squares:

Hence, $P_1 = (\sqrt{5}x + \sqrt{2}y)(\sqrt{5}x - \sqrt{2}y)$

$P_2$ has no real roots and it's not product of two polynomials