For the difference of two squares you can factor using: [tex]a^2 - b^2 = (a + b)(a - b)[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

And for the sum and difference of two cubes:

[tex]a^3 + b^3 = (a+b)(a^2 - ab + b^2)[/tex]

[tex]a^3 - b^3 = (a-b)(a^2 + ab + b^2)[/tex]

How are these formulas found...?

Can it be done with basic algebra (am I missing something really simple)?

For example, it is possible to take [tex]ax^2 + bx + c = 0[/tex] and solve for x to get the quadratic formula. But how do you rework [tex]a^2 - a^2[/tex], or [tex]a^3 \pm b^3[/tex] into their respective formulas? What about with higher exponents (i.e. [tex]a^4 \pm b^4[/tex] or or [tex]a^5 \pm b^5[/tex])?

I realize that the resulting factors must, when multiplied, have middle terms that will completely cancel each other out leaving only [tex]a^n \pm b^n[/tex], but how do you work backwards to find the middle terms of the factors?

-EP

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# Sum/Diff. formulas

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