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Polynomial Factorization - Series 2c

FACTORING BINOMIALS USING DIFFERENCE OF TWO SQUARES

Binomials of the general form m^2 - n^2 can be factored into terms

(m - n)*(m + n).

example5:
9x^2 - 64 = (3x)^2 - (8)^2
= (3x-8)*(3x+8)

example6:
4a^3 - 4a = 4a * (a^2 -1)
= 4a * (a^2 - 1^2)
= 4a * (a - 1)(a + 1)

example7:
x^4 - y^4 = (x^2)^2 - (y^2)^2
= (x^2 - y^2) * (x^2 + y^2)
= (x - y)*(x +y) *(x^2 +y^2)

FACTORING BINOMIALS USING SUM AND DIFFERENCE OF TWO CUBES

Binomials of the general form outlined below can be factored as described:

a^3 + b^3 can be factored into (a + b) * (a^2 - ab + b^2)
a^3 - b^3 can be factored into (a - b) * (a^2 + ab + b^2)