Question 1
<h3>Answer: Choice B.
(x+6)(5ab-4)</h3>
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Explanation:
Note how we have (x+6) show up twice. What we can do is erase both copies to end up with 5ab-4. Then stick parenthesis around that to get (5ab-4). Effectively what is going on here is that we're pulling out the GCF (x+6).
Lastly, tack on the (x+6) we erased earlier to get the factorization of (5ab-4)(x+6). Because multiplication can be done in any order, this means it's the same as (x + 6)(5ab - 4)
We can use the distribution method, the box method, or FOIL to expand that factorization back out and help confirm we have the correct answer.
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Question 2
<h3>Answer: Choice B.
(4b - 7x)(a + 2)</h3>
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Explanation:
We'll use the factor by grouping method.
Pair up the terms, then factor each grouping pair. From there, you'll follow the ideas mentioned in problem 1 to finish things off.
This is what the steps could look like:
4ab - 7ax + 8b - 14x
(4ab - 7ax) + (8b - 14x) ... pair up terms
a(4b - 7x) + 2(4b - 7x) ... factor out GCF from each group
(a + 2)(4b - 7x) ... use the trick done in problem 1
(4b - 7x)(a + 2) .... the order of multiplication doesn't matter
You can use the distribution method, FOIL method, or box method to help confirm the answer.
