7. A = (x + y)^2 - 4y^2
= (x + y - 2y)(x + y + 2y)
= (x - y)(x + 3y)
2. x^4 + 4
= x^4 + 4x^2 + 4 - 4x^2
= (x^2 + 2)^2 - (2x)^2
= (x^2 + 2x + 2)(x^2 - 2x + 2)
3. 4x^4 + 16
= 4(x^4 + 4)
= 4(x^2 + 2x + 2)(x^2 - 2x + 2)
5. x^4 + 4y^4
= x^4 + 4x^2.y^2 + 4y^4 - 4x^2.y^2
= (x^2 + 2y^2)^2 - (2xy)^2
= (x^2 + 2xy + 2y^2)(x^2 - 2xy + 2y^2)