Jeremy had 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?
area of 1st discard = 6x
area of 2nd discard = 3(x-6)
so total area discarde = .....
To determine the total area in square inches of the discarded scraps, we need to find the areas of the two rectangular pieces that Jeremy cut off.
First, he cut 6 inches off the right side of the paper, so the width of the remaining piece is (x - 6) inches. The height remains the same, which is x inches. Therefore, the area of the first scrap is given by (x - 6) * x = x² - 6x square inches.
Next, he cut 3 inches off the top of the remaining piece. The width remains the same, (x - 6) inches, and the new height is (x - 3) inches. Therefore, the area of the second scrap is given by (x - 6) * (x - 3) = (x² - 6x) - 3(x - 6) = x² - 6x - 3x + 18 = x² - 9x + 18 square inches.
To find the total area of the discarded scraps, we simply add the areas of the first and second scraps together:
Total area = (x² - 6x) + (x² - 9x + 18)
= x² - 6x + x² - 9x + 18
= 2x² - 15x + 18 square inches.
Therefore, the expression that represents the total area in square inches of the scraps that Jeremy discarded is 2x² - 15x + 18.