(a-b+c-d)^2 I know how to foil it, but my teacher wants us to use shortcuts. Such like Perfect square trinomial, binomial cubed, Dots, sum of two cubes, diff of two cubes. I can't seem to find any shortcuts. Any help?

Question

(a-b+c-d)^2    I know how to foil it, but my teacher wants us to use shortcuts. Such like Perfect square trinomial, binomial cubed, Dots, sum of two cubes, diff of two cubes. I can't seem to find any shortcuts. Any help?

superhelp101 · Answer

@aum

superhelp101 · Answer

@IMStuck @ganeshie8 @dumbcow any help?

ganeshie8 · Answer

(a-b+c-d)^2   =   ( `(a-b)` + `(c-d)` )^2

ganeshie8 · Answer

use perfect square trinomial formula, expand it out

superhelp101 · Answer

oh okay thanks! :)

ganeshie8 · Answer

(x+y)^2 =  x^2 + 2xy + y^2

superhelp101 · Answer

@aum  do you think you can continue from ganeshie ?

aum · Answer

$$
(a-b+c-d)^2 = (~ (a-b) + (c-d) ~)^2 = (a-b)^2 + 2(a-b)(c-d) + (c-d)^2 = ?
$$

aum · Answer

Think of (a - b) as x  and  (c - d) as y
$$
(a-b+c-d)^2 = (~ (a-b) + (c-d) ~)^2 \
x = (a-b); ~~~ y = (c-d)  \
(x + y)^2 = x^2 + 2xy + y^2 \
(a-b)^2 + 2(a-b)(c-d) + (c-d)^2 = ?
$$

superhelp101 · Answer

okay that makes sense! Let me solve that and let you know what I got.. just a sec ;)

superhelp101 · Answer

it's a2-2ab+b2+2ac-2ad-2bc+2bd+c2-2cd+d2

aum · Answer

Correct.  You can rearrange the term in a different order or leave it as it is.

$a^2 + b^2 + c^2 + d^2 - 2ab + 2ac - 2ad - 2bc + 2bd + 2cd $

superhelp101 · Answer

Thank you! :)

aum · Answer

You are welcome.

superhelp101 · Answer

Oh and also thank you to @ganeshie8 ! You both helped me!