Question

factor the following by taking out the greatest common factor.
$8a^4b^3 + 48a^3b^4 + 32a^4b^4$

question 4
the greatest common factor of the binomial $2x - 8$ is 2. the greatest common factor of the binomial $3x - 3$ is 3. what is the greatest common factor of their product $(2x - 8)(3x - 3)$ when it has been multiplied out?

Explanation:

Step1: Find GCF of coefficients

The coefficients are 8, 48, 32. The greatest common factor is 8.

Step2: Find GCF of $a$-terms

The $a$-terms are $a^4$, $a^3$, $a^4$. The lowest exponent is 3, so GCF is $a^3$.

Step3: Find GCF of $b$-terms

The $b$-terms are $b^3$, $b^4$, $b^4$. The lowest exponent is 3, so GCF is $b^3$.

Step4: Factor out overall GCF

Factor $8a^3b^3$ from each term:
$8a^3b^3(a + 6b + 4ab)$

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Step1: Expand the product

First multiply $(2x-8)(3x-3)$:
$$(2x)(3x) + (2x)(-3) + (-8)(3x) + (-8)(-3) = 6x^2 -6x -24x +24$$

Step2: Simplify the expanded form

Combine like terms:
$6x^2 -30x +24$

Step3: Find GCF of coefficients

Coefficients are 6, -30, 24. GCF is 6.

Step4: Verify variable GCF

The variable terms are $x^2$, $x$, $1$. The lowest exponent of $x$ is 0, so no variable GCF.

Answer:

1. $8a^3b^3(a + 6b + 4ab)$
2. $6$