Factorise : #a^4 + a^2 b^2 + b^4#?

2 Answers
Nityananda
Apr 6, 2018

#(a^2+b^2+ab)(a^2+b^2-ab)#

Explanation:

Given, #a^4+a^2b^2+b^4#
#rArr (a^2)^2+2a^2b^2+(b^2)^2-a^2b^2#
#rArr (a^2+b^2)^2-(ab)^2#
#rArr [(a^2+b^2)+ab][(a^2+b^2)-ab]#
#rArr (a^2+b^2+ab)(a^2+b^2-ab)#

Daniel L.
Apr 6, 2018

See explanation.

Explanation:

#a^4+a^2b^2+b^4=#

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

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

#=(a^2+ab+b^2)(a^2-ab+b^2)#

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