Question

1. the rectangle is made up of two smaller rectangles. which expressions represent of the rectangle in square units? choose all that apply.

a. $6x$
b. $3(x + 2)$
c. $3(2x)$
d. $3(6x)$
e. $3x$
f. $3(x)+3(2)$
g. $3x + 6$

1. the rectangle is made up of two smaller rectangles.

a. write two expressions that each represent the area of the shaded rectangle in square units.
b. use the distributive property to show that the expressions you wrote in part (a) are equivalent.

Explanation:

Problem 3

Step1: Find total height

Total height = $x + 2$ units

Step2: Calculate total area (method1)

Area = $\text{width} \times \text{total height} = 3(x+2)$

Step3: Expand using distributive property

$3(x+2) = 3x + 3(2) = 3x + 6$

Step4: Verify equivalent expressions

Check which options match $3(x+2)$, $3(x)+3(2)$, or $3x+6$.

Part (a) Step1: Find shaded width

Shaded width = $m - 5$ units

Part (a) Step2: Write first area expression

Area = $\text{width} \times \text{height} = 4(m-5)$

Part (a) Step3: Write second area expression

Total area minus unshaded area: $4m - 4\times5 = 4m - 20$

Part (b) Step1: Apply distributive property

Expand $4(m-5)$: $4\times m - 4\times5$

Part (b) Step2: Simplify to show equivalence

$4\times m - 4\times5 = 4m - 20$

Answer:

B. $3(x+2)$
F. $3(x)+3(2)$
G. $3x+6$

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Problem 4