How do you factor special products of polynomials?

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How do you factor special products of polynomials?

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Answer 1 · 2015-01-24T06:13:10

Look for numbers that are perfect squares or perfect cubes.
There are many special products in factoring. Three of the most well-known are
${(x + y)}^{2} = x^{2} + 2 x y + y^{2}$ $(x+y)^2=x^2+2xy+y^2$
and
${(x - y)}^{2} = x - 2 x y + y^{2}$ $(x−y)^2=x-2xy+y^2$
and
$(x + y) (x - y) = x^{2} - y^{2}$ $(x+y)(x−y)=x^2−y^2$

Two less well-known ones are
$x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})$ $x^3+y^3=(x+y)(x^2−xy+y^2)$
and
$x^{3} - y^{3} = (x - y) (x^{2} + x y - y^{2})$ $x^3−y^3=(x−y)(x^2+xy−y^2)$
Note that in an actual problem, x and y can be any number or variable. Hope this helped!

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How do you factor special products of polynomials?

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