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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, x4+4.(x2+2+2x)(x2-2-2x)(x2+2+2x)(x2+2-2x)None of these(x2-2+2x)(x2+2-2x) Q 2: Factorize, x4+16.(x2+4+4x)(x2+4-4x)(x2-4+4x)(x2+4-4x)None of these(x2+4+4x)(x2-4-4x) Question 3: This question is available to subscribers only! Question 4: This question is available to subscribers only!

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