# Math Help - Foil Method

1. ## Foil Method

I know that is first,outer, inner, last but are there other ways to solve using the method?

2. Originally Posted by Russian
I know that is first,outer, inner, last but are there other ways to solve using the method?
Ermmm what do you mean exactly?

If you have a expression $(a+b)(c+d)$, then you could re-write it as $a(c+d) + b(c+d)$, and calculate from there.

So for example:

$(x+5)(x-3)$
$= x(x-3)+5(x-3)$
$= x^2-3x+5x-15$
$= x^2+2x-25$

Essentially, it's the same as foil method. Essential, all ways of expanding the expression are very close to foil method. Can't really go wrong :P.

3. Originally Posted by Russian
I know that is first,outer, inner, last but are there other ways to solve using the method?
To multiply together two expressions, you multiply every term of the first by every term of the last. "FOIL" is just a way of being sure you get all of them and only apply to "two terms times two terms".

For example: to multiply (a+ b)(c+ d) I can use "FOIL": "First" terms, ab; "Outside terms", ad; "Inside" terms, bc; "Last" terms, bd. Adding all of those: ab+ ad+ bc+ bd.

I could have got the same result by using the rule: Multiply the first term in the first expression, a, by each of the terms in the second expression: a(c+ c)= ac+ ad. Then multiply the second term in the first expression by each of the terms in the second expression: b(c+ d)= bc+ bd. Adding those: ac+ ad+ bc+ bd, exactly as above.

If I have 3 terms in, say, the first expression, like (a+ b+ c)(u+ v), I can't use "FOIL" exactly but I can think:
Multiply the first term in the first expression, a, by every term in the second expression- a(u+ v)= au+ av.
Multiply the second term in the first expression, b, by every term in the second expression- b(u+ v)= bu+ bv.
Multiply the third term in the first expression, c, by every term in the second expression- c(u+ v)= cu+ cv.

Now add all of those: (a+ b+ c)(u+ v)= au+ av+ bu+ bv+ cu+ cv.

4. Originally Posted by HallsofIvy
To multiply together two expressions, you multiply every term of the first by every term of the last. "FOIL" is just a way of being sure you get all of them and only apply to "two terms times two terms".

For example: to multiply (a+ b)(c+ d) I can use "FOIL": "First" terms, ab; "Outside terms", ad; "Inside" terms, bc; "Last" terms, bd. Adding all of those: ab+ ad+ bc+ bd.

I could have got the same result by using the rule: Multiply the first term in the first expression, a, by each of the terms in the second expression: a(c+ c)= ac+ ad. Then multiply the second term in the first expression by each of the terms in the second expression: b(c+ d)= bc+ bd. Adding those: ac+ ad+ bc+ bd, exactly as above.

If I have 3 terms in, say, the first expression, like (a+ b+ c)(u+ v), I can't use "FOIL" exactly but I can think:
Multiply the first term in the first expression, a, by every term in the second expression- a(u+ v)= au+ av.
Multiply the second term in the first expression, b, by every term in the second expression- b(u+ v)= bu+ bv.
Multiply the third term in the first expression, c, by every term in the second expression- c(u+ v)= cu+ cv.

Now add all of those: (a+ b+ c)(u+ v)= au+ av+ bu+ bv+ cu+ cv.

thank you again