Question

36x⁴-97x²y²+36y⁴ factorise
Give me answer plz

Answer 1

36x⁴ - 97x²y² + 36y⁴

We can write by splitting 97x²y² in two terms

36x⁴ + 36y⁴ - 72x²y² - 25x²y²

Now we can see

36x⁴ = (6x²)²

36y⁴ = (6y²)²

and 72x²y² = 2(6x²)(6y²)

also 25x²y² = (5xy)²

So we can write 36x⁴ + 36y⁴ - 72x²y² - 25x²y² as

(6x + 6y)² - (5xy)²

Now using a² - b² = (a + b)(a - b)

we get
(6x + 6y)² - (5xy)²

=> (6x + 6y + 5xy)(6x + 6y - 5xy)


Hope it helps dear friend ☺️✌️✌️

Answer 2

Given,

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