Question

1. $81x^{5}y^{8}-18x^{2}y^{3}-90x^{6}y^{6}$

Explanation:

Step1: Rearrange terms by degree

$-90x^6y^6 + 81x^5y^8 - 18x^2y^3$

Step2: Factor out GCF

Find GCF of coefficients: $\gcd(90,81,18)=9$; GCF of $x$-terms: $x^2$; GCF of $y$-terms: $y^3$.
$=-9x^2y^3(10x^4y^3 - 9x^3y^5 + 2)$

Step3: Rearrange inside parentheses

$=-9x^2y^3(-9x^3y^5 + 10x^4y^3 + 2)$
$=9x^2y^3(9x^3y^5 - 10x^4y^3 - 2)$

Answer:

$9x^2y^3(9x^3y^5 - 10x^4y^3 - 2)$ or $-9x^2y^3(10x^4y^3 - 9x^3y^5 + 2)$