Factor x3 + 8.
We have a sum of cubes. Luckily, they're regular math cubes, not gelatinous cubes. Those things are nasty, with a capital "Arg, I'm melting!"
(x)3 + (2)3
According to our general formula, this factors to a binomial that shares its sign with the sum, and has the opposite sign inside the trinomial.
(x + 2)(x2 – 2x + 4)
It looks a lot like that, yep.
Factor x3 – 343.
Is 343 a cube? Hold on while we grab a calculator…oh, yeah, it's 73. We can work with that, then. It will factor to:
(x – 7)(x2 + 7x + 49)
Factor 27x3 – 64y3.
A little bit of rewriting gets us:
(3x)3 – (4y)3
This difference between two cubes transforms into:
(3x – 4y)[(3x)2 + (3x)(4y) + (4y)2]
A little bit of pruning will make this look nicer.
(3x – 4y)(9x2 + 12xy + 16y2)
Factor a9 + b6.
(a3)3 + (b2)3
We put an exponent in your exponent, so you can raise to a power while raising to a power.
(a3 + b2)[(a3)2 – a3b2 + (b2)2]
Simplify it out, while being careful not to mess up the exponents. They'll multiply together in this case.
(a3 + b2)(a6 – a3b2 + b4)
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