Question

Factorize : 4(x+y)^2 -9(x-y)^2​

Answer 1

Answer:

(-x+5y)×(5x-y)

Step-by-step explanation:

(2(x+y)-3(x-y))×(2(x+y)+3(x-y)

(2x+2y-3x+3y)×(2x+2y+3x-3y)

Final answer: (-x+5y)×(5x-y)

Answer 2

Answer:

Step-by-step 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)