#Grateful for any help! <3

23 messages · Page 1 of 1 (latest)

solemn cargoBOT
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dusky blaze
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Grateful for any help! <3

uncut jolt
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What exactly do you need to do?

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I see.
For example, you can start by using the difference of squares formula.

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Although, by "simplify", do you mean just expanding it until it's in usual polynomial form, or factoring it?

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If it's factoring, my advice from above stands.
If it's expanding, then use the binomial expansion for the second term.

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It's a^2 - b^2 = (a - b)(a + b).

dusty bronzeBOT
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@dusky blaze has given 1 rep to @uncut jolt

uncut jolt
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Alright. Try that, then. What do you get?

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Well, you can use the binomial expansion, but then it will be really difficult to factor it.

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If we want to factor, better to use the difference of squares formula if possible, or any others similar to it.

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Note that you might need to use it more than once.

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Well, you'll see when you do it.

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Well, that's just expanding.

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Let me show one appication of the difference of squares formula.
x^4 - (x - 2)^4 = (x^2 - (x - 2)^2)(x^2 + (x - 2)^2)

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Notice how you still have a difference of squares in the first factor. So, you can use the formula again.

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Again, that's expanding, not factoring. Still incorrect if we want to do that, though.

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Let's continue factoring. We use the formula once:
x^4 - (x - 2)^4 = (x^2 - (x - 2)^2)(x^2 + (x - 2)^2)
Then we use it again for the first factor:
x^4 - (x - 2)^4 = (x - (x - 2))(x + (x - 2))(x^2 + (x - 2)^2)
Can you now simplify the expression on the right?

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Well, that can't be, obviously. That's just 128x^4.
We have:
x^4 - (x - 2)^4 = (x - (x - 2))(x + (x - 2))(x^2 + (x - 2)^2)
We simplify thefactors on the right.
x^4 - (x - 2)^4 = 2(2x - 2)(2x^2 - 4x + 4)
Then we factor 2 from the second and third factors.
x^4 - (x - 2)^4 = 8(x - 1)(x^2 - 2x + 2)
And that's the factorisation.

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You just need some practice with using the usual formulas.

dusty bronzeBOT
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@dusky blaze has given 1 rep to @uncut jolt

uncut jolt
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No worries! Good luck with that, by the way.