Question

Factorize : 4(x+y)^2 -9(x-y)^2​

Answer 1

Explanation:

`4(x+y)^(2) - 9(x-y)^(2)=4[x^(2)+2xy+y^(2)]-9[x^(2)-2xy+y^(2)]\\\\=4x^(2)+4*2xy + 4y^(2)-9x^(2)-2xy*(-9)+y^(2)*(-9)\\\\= 4x^(2)+8xy+4y^(2)-9x^(2)+18xy-9y^(2)\\\\= 4x^(2)-9x^(2) + 8xy + 18xy +4y^(2) - 9y^(2)\\\\= -5x^(2) + 26xy - 5y^(2)`

= -5x² + 25xy + xy - 5y²

= 5x(-x + 5y) - y(-x +5y)

= (-x + 5y)(5x - y)