Question

Factorise this 36x⁴-97x²y²+36y⁴

Answer 1

Given,

$36x^{4} - 97x^{2}y^{2} + 36y^{4} \\ \\ = 36x^{4}+ 36y^{4} - 97x^{2}y^{2} \\ \\ = (6x)^{2} + (6y)^{2} + 2*6x*6y \ - 72x^{2}y^{2} + 72x^{2}y^{2} - 97x^{2}y^{2} \\ \\ = (6x + 6y )^{2} - 25x^{2}y^{2} \\ \\ = (6x + 6y )^{2} - (5xy) \\ \\ =(6x + 6y - 5xy) (6x + 6y + 5xy) \\ \\ = \textbf{(6x + 6y - 5xy) (6x + 6y + 5xy)}$