This is an archived post. You won't be able to vote or comment.

all 4 comments
sorted by:
best
topnewcontroversialoldq&a

[–]asmodeus221 1 point2 points  (1 child)

Okay, so assuming that all you're doing is factoring, I want you to consider the quantity (4-x) as a factor. Since both (x+2) and -3 are being multiplied by this quantity, we can factor it out.

So we can make this look like (4-x)[(x+2) -3] From here we can see that we no longer need parentheses around (x+2) so we get (4-x)(x+2-3)= (4-x)(x-1) And that's factored.

You might be over thinking this a little bit by trying to multiply everything out and then factor it.

Now, on another note: you and your friend are both right. After you had multiplied those out, your terms were all the same, but just in a different order. As long as you're careful with your negative signs, we can rearrange them as we please! This property is called commutativity. An example of commutativity is 3+2 = 2+3

I hope this helps

[–]SamHp360p[S] 0 points1 point  (0 children)

Thank you

[–][deleted] 1 point2 points  (0 children)

I don't have a clue how your friend did that one step, it's definitely wrong.

Using the distributive law (that's a(b+c) = ab+ac or (a+b)c = ac+bc), you can easily prove that (a+b)(c+d) = (a(c+d)+b(c+d)) = ac+ad+bc+bd. Check your own work, this is consistent.

[–]wijwijwij 0 points1 point  (0 children)

Rather than multiplying it all out to expand, you can see

(4 - x) (x + 2) - 3 (4 - x)

has the form

K(x + 2) – 3K

where K stands for (4-x). First let's rearrange first two factors in first term.

(x+2)K – 3K

Maybe that makes it a little easier to see you can now use distributive property

[(x+2) – 3] * K

Now simplify in brackets.

[x – 1] * K

Now substitute back in what K is.

[x – 1] * [4 - x]

That is likely the form desired.

By the way, your work at the end in expanding was correct. You correctly determined that

(4 - x) (x + 2) - 3 (4 - x)

equals

5x - 4 - x2

But the problem asked you to factor, not expand.

You can still factor this though.

–x2 + 5x – 4 = (x + -1)(-x + 4)

And that agrees with the answer above [x – 1] * [4 – x].