Question

a^4+5a^2 b^2+9b^4 a^4-23a^2+1

Answer 1

a^4+5a^2b^2+9b^4

=a^4+6a^2b^2+9b^4-a^2b^2

=(a^2+3b^2)^2-(ab)^2

=[(a^2+3b^2)-(ab)][(a^2+3b^2)+(ab)]

=(a^2+3b^2-ab)(a^2+3b^2+ab);

a^4-23a^2+1

=a^4+2a^2+1-25a^2

=(a^2+1)^2-(5a)^2

=(a^2-5a+1)(a^2+5a+1).