Expand the left side of the equation:
(x+y)(x-y) + (y+a)(y-a)= x^2 - y^2 + y^2 - a^2= x^2 - a^2
Expand the right side of the equation:
(x-a)(x+a)= x^2 - a^2
Therefore, the equation is true as both sides simplify to x^2 - a^2.
Expand the left side of the equation:
(x+y)(x-y) + (y+a)(y-a)
= x^2 - y^2 + y^2 - a^2
= x^2 - a^2
Expand the right side of the equation:
(x-a)(x+a)
= x^2 - a^2
Therefore, the equation is true as both sides simplify to x^2 - a^2.