Question 5: Factorize 4 x 4 + 81

a 4 + a 2 b 2 + b 4 or a 4 + 4b 4 type expressions

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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