Answers:
Factored Form is (x+4)(x+2)
Expanded Form is x^2+6x+8
----------------------------------------------------------
----------------------------------------------------------
Step-by-step explanation:
The factored form is simply a matter of reading off the values from the given image. There isn't much work to show here.
Along the left side we have x and 4 so x+4 is one of the factors. Along the bottom we have x and 2, so x+2 is another factor
The two factors are (x+4) and (x+2) so that's why the factored form is (x+4)(x+2)
-------------------------------
Let's expand out the factored form
The overall rectangle is broken up into four parts. I'll label the four smaller rectangles as...
Rectangle A in the upper left corner (this rectangle is x by x)
Rectangle B in the upper right corner (this rectangle is 2 by x)
Rectangle C in the lower left corner (this rectangle is x by 4)
Rectangle D in the lower right corner (this rectangle is 2 by 4)
The idea is that adding the areas of rectangles A through D leads us to the overall area for this largest rectangle.
Area of Rectangle A = (length)*(width) = x*x = x^2
Area of Rectangle B = (length)*(width) = 2*x = 2x
Area of Rectangle C = (length)*(width) = x*4 = 4x
Area of Rectangle D = (length)*(width) = 2*4 = 8
Notice we have the like terms 2x and 4x (areas of rectangle C and D respectively). They combine to 2x+4x = 6x
So after adding all the individual areas and combining like terms, we arrive at the fully expanded form of x^2+6x+8