Answer
a) left area is $(2x+2)(x+2)$, right area is $(x+1)(2x+4)$
b) Yes
c) The same trinomial can have different factors that allow the trinomial to be factored differently.
Work Step by Step
a)
Left area: One side is $(2x+2)$ and the other side is $(x+2)$.
Right area: One side is $(x+1)$ and the other side is $(2x+4)$.
b)
$(2x+2)(x+2)$
$2x^2+2*2x+2*x+2*2$
$2x^2+4x+2x+4$
$2x^2+6x+4$
$(x+1)(2x+4)$
$x*2x+x*4+1*2x+1*4$
$2x^2+4x+2x+4$
$2x^2+6x+4$
$2x^2+6x+4=2x^2+6x+4$
c)
$2x^2+6x+4$
$2(x^2+3x+2)$
$2(x^2+2x+x+2)$
$2*[x(x+2)+(x+2)]$
$2*[x(x+2)+1(x+2)]$
$2*(x+2)(x+1)$
If we break down the factors of the trinomial, we have $2$, $(x+2)$, and $(x+1)$. The two different pairs of binomials use the factor of $2$ differently.
$(2x+2)(x+2)$
$[2*(x+1)](x+2)$
$2*(x+1)(x+2)$
$2(x+1)(x+2)$
$(x+1)(2x+4)$
$(x+1)*[2*(x+2)]$
$(x+1)*2*(x+2)$
$2(x+1)(x+2)$
