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Middle/High School Algebra, Geometry, and Statistics (AGS)
3.7 Factorization: Completing the Square

Example: Factorize, x4+324.
Solution:
Given that, x4+324.
We can write this as,
= (x2)2+(18)2.
Here a = x2 and b = 18, we don't have 2ab term
Therefore, 2ab = 2.x2.18 = 36x2.
We add 36x2 and subtract 36x2, in the above equation, we get
= x4+324+36x2-36x2
= (x2)2+(18)2.+2.x2.18-36x2
This is in the form of (a+b)2 = a2+2.a.b+b2
= (x2+18)2-36x2
We can write this as
= (x2+18)2-(6x)2
= This is in the form of a2-b2 = (a+b)(a-b)
= (x2+18+6x)(x2+18-6x)

Directions: Solve the following problems. Also write at least ten examples of your own.
Q 1: Factorize, 3x4+12.
None of these
3(x2-2x+2)(x2-2x+2)
3(x2+2x+2)(x2+2x+2)
3(x2+2x+2)(x2-2x+2)

Q 2: Factorize, 4x4+81.
None of these
(2x2+6x+9)(2x2-6x+9)
(2x2+6x+9)(2x2+6x+9)
(2x2-6x+9)(2x2-6x+9)

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