Question

11a. $(x + y)^2 = x^2 + 2xy + y^2$

Explanation:

Step1: Rewrite square as product

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

Step2: Apply distributive property (FOIL)

$(x+y)(x+y) = x(x+y) + y(x+y)$

Step3: Distribute terms further

$x(x+y) + y(x+y) = x^2 + xy + yx + y^2$

Step4: Combine like terms

$x^2 + xy + yx + y^2 = x^2 + 2xy + y^2$

Answer:

The identity $(x+y)^2 = x^2 + 2xy + y^2$ is verified.