Question

Is algebra.

Answer 1

Question 1

Answer: Choice B.  (x+6)(5ab-4)

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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

Answer: Choice B.  (4b - 7x)(a + 2)

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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.

Answer 2

Answer:

1) b   2) b

Step-by-step explanation:

1) Both expressions have (x+6). Rearrange them and you'll have one expression as (x+6) and the other as (5ab-4).

2) (4b - 7x)(a + b) factors to be 4ba + 8b - 7ax - 14x, which can be rearranged to 4ab - 7ax + 8b - 14x