Question

(a + b - c)(a + b + c)

Answer 1

Here's why I dislike the FOIL bit so much: as soon as you move away from multiplying two binomials, people who only know FOIL are stuck. Better to understand it as multiple applications of the distributive property, in my opinion.

\[p(q+r) = p*q + p*r\]\[(p+q)(r+s) = p(r+s) + q(r+s) = p*r + p*s + q*r + q*s\]\[(p+q+r)(s+t+u) = p(s+t+u) + q(s+t+u) + r(s+t+u) =\]\[=p*s + p*t + p*u + q*s + q*t + q*u + r*s + r*t + r*u\]And so on...

Give it a shot! In words, take each piece of the first thing, multiply by each piece of the second thing, add up all the results.

Answer 2

I have a^2 b^2 a^2 + -c^2. I know im wrong

Answer 3

\[(a+b-c)(a+b+c) = a(a+b+c) + b(a+b+c) - c(a+b+c)\]That's the first use of the distributive property. Do you see how/why I did that?

Answer 4

how would I write that?

Answer 5

how would you write that? just like I did.

Answer 6

but that's just the first step.

Answer 7

Next, you have to use the distributive property again to get rid of all of the ( )'s

For example, the first term:

\[a(a+b+c) = a*a + a*b + a*c = a^2 + ab + ac\]

Answer 8

Now you do that with the other two products...

Answer 9

b^2 + ba + bc c^2 + cb +ca?

Answer 10

Yes! Now add up all the bits and pieces.

Answer 11

Remember, that last group had a \(-c\) in front of it, not a \(+c\), so you'll be subtracting them, not adding.

Answer 12

im stuck on the part

Answer 13

\[(a+b-c)(a+b+c) = a(a+b+c)+b(a+b+c) - c(a+b+c) = \]\[a^2+ab + ac + b^2 + ab + bc - c^2 - ac -bc = \]

Answer 14

another approach: (x-y)(x+y) = (x^2 - y^2)

then do the squares and simplify where possible.

Answer 15

idk

Answer 16

\[a^2+ab+ac+b^2 + ab + bc - c^2 -ac -bc\]collect all the squared terms up front:
\[a^2+b^2-c^2 + ab + ac + ab + bc - ac - bc\]Now collect all of the ab terms
\[a^2+b^2-c^2 + ab + ab + ac + bc - ac - bc\]
\[a^2+b^2-c^2 + 2ab + ac+bc-ac-bc\]Now collect the ac terms
\[a^2+b^2-c^2 + 2ab + ac - ac + bc - bc\]\[a^2+b^2-c^2+2ab+bc-bc\]now collect the bc terms\[a^2+b^2-c^2+2ab\]

Answer 17

if you don't know how to do something, don't use that stupid "idk" — say "I don't know" or "I don't understand" and ask for an explanation. Sitting there and saying "idk" will not help you learn. Taking an active part will. You'll make plenty of mistakes along the way. That's fine, essential even.

Answer 18

There's nothing magical about what we did here. It's straightforward, and a bit tedious. Easy to make mistakes. One of the most valuable things you can learn in math classes, in my opinion, is how to work carefully and accurately, with attention to all the little details that can make the difference between a correct answer and an incorrect one. That's a skill that will be useful in just about anything worth doing, whether or not it involves math.