Question

4x^4+9y^4+11x^2y^2 factorise it

Answer 1

Answer:

$4x^4+9y^4+11x^2y^2=(2x^2-xy+3y^2)(2x^2+xy+3y^2)$

Step-by-step explanation:

Formula used:

$1.\:a^2-b^2=(a+b)(a-b)$

$2.\:(a+b)^2=a^2+b^2+2ab$

consider

$4x^4+9y^4+11x^2y^2$

Add and subtract $x^2y^2$

$=4x^4+9y^4+11x^2y^2+x^2y^2-x^2y^2$

$=[4x^4+9y^4+12x^2y^2]-x^2y^2$

$=[(2x^2)^2+(3y^2)^2+2(2x^2)(3y^2)]-(xy)^2$

$=[2x^2+3y^2]^2-(xy)^2$ (using formula (2))

$=(2x^2+3y^2-xy)(2x^2+3y^2+xy)$ (using formula (1))

$=(2x^2-xy+3y^2)(2x^2+xy+3y^2)$