a square piece of gift wrapping paper with a side length of x inches that he used to wrap a present. First he cut 6 inches off the right side of the paper and discarded the rectangular scrap. Next he cut 3 inches off the top of the paper and again discarded the rectangular scrap. What expression represents the total area in square inches of the scraps that he discarded?
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A1 = x * x = X^2 = Area before cutting.
L = x-6 = Length after cutting.
W = x-3 = Width after cutting.
A2 = L*W = (x-6)*(x-3) = x^2 - 3x -6x + 18 = x^2 - 9x + 18. = Area remaining.
A1 - A2 = x^2 - (x^2 -9x+18) = 9x-18 = 9(x-2) in^2 discarded.
To find the expression representing the total area of the scraps that were discarded, we need to calculate the area of the rectangular scrap from cutting the right side and the area of the rectangular scrap from cutting the top.
First, let's find the area of the rectangular scrap from cutting the right side. We know that the original length of the paper is x inches, and 6 inches were cut off. Therefore, the length of the rectangular scrap is 6 inches. The width of the rectangular scrap remains the same, which is x inches. So, the area of the rectangular scrap from cutting the right side is 6 inches multiplied by x inches, which is 6x square inches.
Next, let's calculate the area of the rectangular scrap from cutting the top. We know that the original length of the paper is x inches, and 3 inches were cut off. Therefore, the length of the rectangular scrap is 3 inches. The width of the rectangular scrap becomes (x - 6) inches since 6 inches were already cut off from the right side. So, the area of the rectangular scrap from cutting the top is 3 inches multiplied by (x - 6) inches, which is 3(x - 6) square inches.
To find the total area of the scraps that were discarded, we simply add the two areas together:
Total area of scraps = Area of scrap from cutting the right side + Area of scrap from cutting the top
= 6x + 3(x - 6)
= 6x + 3x - 18
= 9x - 18 square inches
Therefore, the expression representing the total area in square inches of the scraps that were discarded is 9x - 18.