Question

How do i solve (x+2)^2 with given identity? My teacher wants me to show how to solve it using multiplication and given identity... i know how to solve it with foil and i get the answer and show it like this
Foil: (x+2)^2
(x+2)(x+2)
x^2+2x+2x+4
x^2+4x+4


But given identity i don't know pls help i've been trying to figure it out for hours

Answer 1

Is the identity $(x+a)^2 = x^2 + 2ax + a^2$  ?

If so, all you have to do is recognize that in your example, a = 2
Substitute into the identity

$(x+2)^2 = x^2 + 2(2)x + 2^2 = x^2 +4x + 4$

Recognizing an identity can be helpful in that it can save time when expanding.