Question

1. 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? 1 $x^{2}+23x - 7$ 2 $x^{2}+13x - 7$ 3 $7x^{2}+23x - 7$ 4 $7x^{2}+13x - 7$

Explanation:

Step1: Find area of large rectangle

The area formula for a rectangle is $A = l\times w$. For the large rectangle with length $l=(3x + 7)$ and width $w=(3x - 1)$, we use the FOIL method.

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Step2: Find area of cut - out rectangle

For the cut - out rectangle with length $l = 2x+5$ and width $w=x$, the area is $A_{2}=x(2x + 5)=2x^{2}+5x$.

Step3: Find area of shaded region

The area of the shaded region $A$ is the area of the large rectangle minus the area of the cut - out rectangle.

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Answer:

D. $7x^{2}+13x - 7$