Question

Q.4 a) If a= x+y and b= x-y , show that I) (a+b)²= 4x² ii) ( a-b)²= 4y²​

Answer 1

Below.

Explanation:

i) (a + b)^2 = a^2 + 2ab + b^2

= (x + y)^2 + 2(x + y)(x - y) + (x - y)^2

= x^2 + 2xy + y^2 + 2(x^2 - y^2) + x^2 - 2xy + y^2

= x^2 + 2x^2 + x^2 + y^2 - 2y^2 + y^2 + 2xy - 2xy

= 4x^2.

ii) (a - b)^2 = a^2 + b^2 - 2ab

= (x + y)^2 + (x - y)^2 - 2 - 2(x^2 - y^2)

= x^2 + 2xy + y^2 + x^2 - 2xy + y^2 - 2x^2 + 2y^2

= x^2 + x^2 - 2x^2 + y^2 + y^2 + 2y^2 + 2xy - 2xy

= 4y^2.