Factoring

[afvatcha]

What would(a-b)^4 look like completely factored.

I assumed it would be (a-b)(a+b)(a-b)(a+b).

Where did I go wrong???

[RonPurewal]

What would(a-b)^4 look like completely factored.

I assumed it would be (a-b)(a+b)(a-b)(a+b).

Where did I go wrong???

nope. that would be (a^2 - b^2) squared, which doesn't work out to a^4 - b^4. try multiplying it out if you don't see this.

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you CAN use the difference of squares formula, since a^4 is the square of a^2 and b^4 is the square of b^2. therefore, your pattern factors into
(a^2 - b^2)(a^2 + b^2)

now, the first of these is the traditional difference of squares. the second, however, doesn't factor, at all, into anything.

so we have the final product:
(a - b)(a + b)(a^2 + b^2)

[chintanjpatel]

can we write (a-b)^2 = a^2 - B^2. i guess not. so how can we write (a-b)^4= (a^2-b^2)^2.

[StaceyKoprince]

Chintan, I'm not quite sure from you're wording, but I think when you say "how can we write..." you're saying that you know that we can't actually do it. If you're actually asking how we can write that, let me know.