00:01
Problem, what we're being asked to do is to write an expression to represent the area of the shaded region.
00:07
Well, notice how we have this outside rectangle that i'm now going to label in green, and then we have this inside rectangle that's in white that i'm going to shade in blue.
00:19
So in order to find that red shaded region, because it's not a regular polygon shape, what we're going to do is we're going to find the area of the whole rectangle, the one that's in green, and then what we're going to do is we're going to subtract that by the area of the rectangle that i just highlighted in blue.
00:37
Because then if we take the whole area and we subtract out this piece right here, then we would get the remainder of that rectangle, which is in red.
00:46
Well, because the whole rectangle, or because it's rectangle, to find the area we multiply the length times the width.
00:53
So in this case, the length is 2x minus 3, and the width is x plus 7.
00:58
Well, the inner shaded area in blue is also a rectangle.
01:04
So again, to find its area, we'll multiply the length times the width.
01:07
So we'll do x plus 2 times x plus 3.
01:10
Perfect.
01:11
Now we have an expression for the shaded area.
01:14
So now we just need to simplify it.
01:16
So to multiply our first two binomials, we're going to use the foil method.
01:20
Well, 2x times x is 2x squared.
01:23
2x times 7 is positive 14x.
01:25
Negative 3 times x is negative 3x and negative 3 times 7 is negative 21...
