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Example:
Factorize, x^{4}+324. Solution: Given that, x^{4}+324. We can write this as, = (x^{2})^{2}+(18)^{2}. Here a = x^{2 }and b = 18, we don't have 2ab term Therefore, 2ab = 2.x^{2}.18 = 36x^{2}. We add 36x^{2} and subtract 36x^{2}, in the above equation, we get = x^{4}+324+36x^{2}36x^{2} = (x^{2})^{2}+(18)^{2}.+2.x^{2}.1836x^{2} This is in the form of (a+b)^{2} = a^{2}+2.a.b+b^{2} = (x^{2}+18)^{2}36x^{2} We can write this as = (x^{2}+18)^{2}(6x)^{2} = This is in the form of a^{2}b^{2} = (a+b)(ab) = (x^{2}+18+6x)(x^{2}+186x) Directions: Solve the following problems. Also write at least ten examples of your own. 