d Question 4: Factorize a 4 + 3a 2 b 2 + 4b 4 | Job Exam Rare Mathematics (JEMrare) - Solved MCQs

Question 4: Factorize a 4 + 3a 2 b 2 + 4b 4

Question 4: Factorize $a^4+3a^2b^2+4b^4$

Factorization rules —

Solution:

Given expression is ;

$a^4+3a^2b^2+4b^4$

This can be written as;

$=a^4+3a^2b^2+4b^4 +a^2b^2-a^2b^2$ (adding and subtracting $a^2b^2$ )

$=a^4+4a^2b^2+4b^4 -a^2b^2$

Arranging to form $a^2+2(a)(b)+b^2$ form for first three terms;

$=(a^2)^2+2(a^2)(2b^2)+(2b^2)^2-a^2b^2$

Taking $(a+b)^2$ form for fist three terms in this way;

$=(a^2+2b^2)^2 -a^2b^2$

$=[(a^2+2b^2)^2 -a^2b^2 ]$

This is now $a^2-b^2$ form- writing in brackets;

$=[(a^2+2b^2)^2 -(ab)^2 ]$

Applying $(a+b)(a-b)$ form;

$=[(a^2+2b^2)+ab ] [(a^2+2b^2)-ab ]$

$=[a^2+2b^2+ab ] [a^2+2b^2-ab ]$

You may submit a MCQ or maths problem with solution tips here in the comment box below! If you could not solve anyone, you may submit a MCQ or maths problem without solution as well. We will try our level best to solve it for you! Cancel Reply

All original content on these pages is fingerprinted and certified by Digiprove

日本語

You may submit a MCQ or maths problem with solution tips here in the comment box below! If you could not solve anyone, you may submit a MCQ or maths problem without solution as well. We will try our level best to solve it for you! Cancel Reply

Pages

Archives

Categories

Meta

Question 4: Factorize a 4 + 3a 2 b 2 + 4b 4

You may submit a MCQ or maths problem with solution tips here in the comment box below! If you could not solve anyone, you may submit a MCQ or maths problem without solution as well. We will try our level best to solve it for you! Cancel Reply

Meta

Subscribe to jemrare.com