(x + y + 2z)(x + y) can be expressed as

Correct option is C

Given:

Given expression (x + y + 2z)(x + y)

Formula Used:

​$$(a+b+c)^{2}= a^{2}+b^{2}+c^{2} +2(ab+bc+ac)$$​​

Solution:

(x + y + 2z)(x + y)

Expanding the expression

= $$x^2 +xy +xy +y^2 + 2xz +2yz$$​​

= $$x^2 +y^2 +2xy + 2xz +2yz$$​​

= $$x^2 +y^2 +2xy + 2xz +2yz +z^2 -z^2$$​​

= $$x^2 +y^2 +z^2+2xy + 2xz +2yz -z^2$$​​

= $$(x+y+z)^2 -z^2$$​​