In the diagram at the right, the dimensions of the large rectangle are (3x - 1) by (3x + 7) units. The dimensions of the cut-out rectangle are x by 2x + 5 units. Which choice expresses the area of the shaded region, in square units?

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Mathematics

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1 November, 17:43

In the diagram at the right, the dimensions of the large rectangle are (3x - 1) by (3x + 7) units. The dimensions of the cut-out rectangle are x by 2x + 5 units. Which choice expresses the area of the shaded region, in square units?

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Emilia · Answer 1

Large Rectangle

(3x - 1) (3x + 7)

9x² + 21x - 3x - 7

9x² + 18x - 7

Cut - Out Rectangle

x (2x + 5)

x (2x) + x (5)

2x² + 5x

Large Rectangle - Cut - Out Rectangle

(9x² + 18x - 7) - (2x² + 5x)

9x² - 2x² + 18x - 5x - 7

5x² + 13x - 7