## Algebra 1

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.
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. $(2x+2)(x+2)$ $[2*(x+1)](x+2)$ $2*(x+1)(x+2)$ $2(x+1)(x+2)$ $(x+1)(2x+4)$ $(x+1)*[2*(x+2)]$ $(x+1)*2*(x+2)$ $2(x+1)(x+2)$