Question 1065139
{{{x}}}= length of the side of the larger square workout mat
{{{y}}}= length of the side of the smaller square workout mat
 
a. We calculate the surface area of each mat
{{{x*x=x^2}}}= surface area of the larger square workout mat
{{{y*y=y^2}}}= surface area of the smaller square workout mat
{{{highlight(x^2-y^2)}}}= binomial that represents how much more area the larger mat has than the smaller mat.
 
b. {{{highlight(x^2-y^2=(x+y)*(x-y))}}} is the factoring
{{{(x+y)}}} means the sum of the side lengths of the two mats
{{{(x-y)}}} means the difference of the side lengths of the two mats
Here is how to visualize those factors with the mats placed side by side.
{{{drawing(400,300,-0.5,7.5,-0.8,5.2,
rectangle(0,0,5,4.95),
red(rectangle(5.05,0,7,2)),
locate(0.07,2.8,x),locate(2.3,0.3,x),
locate(2.1,2.9,larger),locate(2.3,2.5,mat),
locate(5.5,1.4,red(smaller)),locate(5.8,1,red(mat)),
locate(5.07,1.2,red(y)),locate(5.9,0.35,red(y)),
arrow(3,-0.4,0,-0.4),arrow(4,-0.4,7,-0.4),
locate(3.15,-0.25,(x+y)),locate(5.1,3.65,(x-y)),
arrow(5.45,3.7,5.45,5),arrow(5.45,3.3,5.45,2)
)}}}
 
c. {{{x^2=4y^2}}} says that the larger mat has 4 times the area of the other mat.
Substituting {{{4y^2}}} for {{{x^2}}} in the binomial expression {{{x^2-y^2}}} ,
we get {{{4y^2-y^2=highlight(3y^2)}}} .