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Middle/High School Algebra, Geometry, and Statistics (AGS)
3.5 Factorization: (a-b)3

Example:
Factorize, 8a3-60a2+150a-125.

Solution:
Given that, 8a3-60a2+150a-125.
We can write this as,
(2a)3-3.(2a)2.5+3.2a.(3)2-(5)3.
This is the form of a3-3.a2.b+3.a.b2-b3 = (a-b)3.
Here a = 2a and b = 5, substitute these values in the equation we get,
= (2a-5)3.

Directions: Solve the following problems. Also write at least ten examples of your own.
Q 1: Factorize, a3-6a2b+12ab2-8b3.
(a-2b)2
None of these
(a+2b)3
(a-2b)3

 Q 2: Factorize, a3-9a2b+27ab2-27b3.
(a+3b)3
(a-3b)2
(a-3b)3
None of these

Q 3: Factorize, 27a3-54a2b+36ab2-8b3.
(3a-2b)3
(3a-2b)2
(3a+2b)3
None of these

 Q 4: Factorize, 27a3-27a2b+9ab2-b3.
None of these
(3a-b)2
(3a-b)3
(3a+b)3

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 Question 6: This question is available to subscribers only!


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