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Middle/High School Algebra, Geometry, and Statistics (AGS)
3.2 Factorization: a3 - b3

Example:
Factorize, 27x3-8.
Solution:
Given that, 27x3-8.
We can write this as,
= (3x)3-(2)3
This is in the form of a3-b3 = (a-b)(a2+ab+b2)
here, a = 3x and b = 2, substitute these value in the above equation, we get
= (3x-2)(9x2+6x+4)
Directions: Solve the following problems. Also write at least ten examples of your own.
Q 1: Factorize, x3-8.
(x-2)(x2-2x+4)
(x-2)(x2+2x+4)
(x+2)(x2+2x+4)
None of these

 Q 2: Factorize, 125x3-27.
(5x+3)(25x2+15x+9)
(5x-3)(25x2+15x+9)
None of these
(5x-3)(25x2-15x+9)

Q 3: Factorize, 27x3-64.
(3x-4)(9x2-12x+16)
(3x-4)(9x2+12x+16)
None of these
(3x+4)(9x2+12x+16)

 Q 4: Factorize, 27x3-216.
(3x-6)(9x2+18x+6)
None of these
(3x-6)(9x2-18x+6)
(3x+6)(9x2+18x+6)

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