Question

e assignment - factoring polynomials
factor out the gcf in the following polynomial.
$40a^{2}b^{2}-30a^{6}b^{6}+30ab - 20a^{6}b$
$40a^{2}b^{2}-30a^{6}b^{6}+30ab - 20a^{6}b=\square$

Explanation:

Step1: Find GCF of coefficients

The coefficients are 40, -30, 30, -20.
The greatest common factor of these numbers is 10.

Step2: Find GCF of $a$-terms

The $a$-terms are $a^2$, $a^6$, $a^1$, $a^6$.
The lowest exponent of $a$ is 1, so GCF is $a$.

Step3: Find GCF of $b$-terms

The $b$-terms are $b^2$, $b^6$, $b^1$, $b^1$.
The lowest exponent of $b$ is 1, so GCF is $b$.

Step4: Combine GCFs

The overall GCF is $10ab$.

Step5: Divide each term by GCF

$\frac{40a^2b^2}{10ab} = 4ab$, $\frac{-30a^6b^6}{10ab} = -3a^5b^5$, $\frac{30ab}{10ab} = 3$, $\frac{-20a^6b}{10ab} = -2a^5$

Step6: Write factored form

Factor out $10ab$ from the polynomial.
$10ab(4ab - 3a^5b^5 + 3 - 2a^5)$

Answer:

$10ab(4ab - 3a^5b^5 + 3 - 2a^5)$