Question

Help with this please.

Find the product mentally.

[(x + 1)(x - 1)]2
=
1. x4 + 2x2 - 1
2. x2 - 1
3. x4 - 2x2 + 1

Help please!

Answer 1

@phi @dumbcow any help please?

Answer 2

They want you to memorize how to factor a "difference of squares"
Does that ring any bells?
How do you factor \( (a^2 - b^2) \)?

Answer 3

and they also want you to know how to expand the square
\[ (a-b)2 \]
which has a very simple pattern (that they want you to memorize... so you can just write it down)

Answer 4

Well it would be... (a + b) (a - b) ?

Answer 5

yes. Now look at your problem.... you are going the "other way"

Answer 6

So instead it would be... (a - b) (a + c) or is it going to be.. (b + a) ( b - a) ?

Answer 7

(x+1)(x-1)
that is like
(a+b)(a-b)
what does it multiply out to ?

Answer 8

x^2 + 1 x + 1x -1? Is that correct? Sorry I am horrible with math

Answer 9

So then that would be
"x^2+2x-1?"

Answer 10

you know
(a^2 - b^2) = (a+b)(a-b)
that works both ways:
(a+b)(a-b) = (a^2 - b^2)

Answer 11

so you should look at
(x+1)(x-1) and say "aha! those are the factors for a difference of squares"

Answer 12

but wait it's squared as a whole! ahaaaa. So does that mean it would be x^4+2x^2-1....?

Answer 13

the idea is in steps:
(x+1)(x-1) is (x^2 - 1)
but we want
\( (x^2-1)^2 \)
we use this pattern: \( (a-b)^2 = a^2 -2ab + b^2 \)
can you see what the answer is (with a being x^2 and b being 1)