Question 5: Factorize 4 x 4 + 81

Question 5: Factorize 4x^4+81

Factorization exercises — 

Solution:

 

Given expression is

4x^4+81

Can be written as;

= (2x^2)^2+(9)^2

Adding and subtracting 2(2x^2)(9);

=(2x^2)^2+2(2x^2)(9)+(9)^2-2(2x^2)(9)

First three terms are of (a+b)^2= a^2+2(a)(b)+b^2. so;

=(2x^2+9)^2-36x^2

Taking whole square of second term as well;

=(2x^2+9)^2-(6x)^2

This is now a^2-b^2-(a+b)(a-b) form, so;

=(2x^2+9+6x)(2x^2+9-6x)

Rearranging;

=(2x^2+6x+9)(2x^2-6x+9)

 

Is the factorization!

 

 

 


 

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