A rectangle has an area of $(4 x + 12)$ square units. Write three multiplication expressions that can represent the product of the length and the width of the rectangle

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Solution

Hint: Area of rectangle = length $\times$ width
Step 1: First expression:
We have given a rectangle with area $(4 x + 12)$ square units.
Firstly we will find the factors of $(4 x), (12)$
$4 x = 2 \times 2 \times x 12 = 2 \times 2 \times 3$
Using the distributive property to factor out the common term $2$
$(4 x + 12) = 2 (2 x) + 2 (6) {∵ R e w r i t e t h e e x p r e s s i o n}$
First expression $= 2 (2 x + 6)$
Step 2: Second expression: Now again Using the distributive property to factor out $4$ of $(4 x + 12)$
$(4 x + 12) = 4 (x) + 4 (3)$
Second expression = $4 (x + 3)$
Step 3: Third expression:
We have given expression as $(4 x + 12)$
We will factorise both terms
$4 x = \frac{1}{2} \times 4 x 12 = \frac{1}{2} \times 6 \times 4$
Using the distributive property to factor out $\frac{1}{2}$
$(4 x + 12) = \frac{1}{2} (4 x) + \frac{1}{2} (6 \times 4) {R e w r i t e t h e e x p r e s s i o n}$
Third expression = $\frac{1}{2} (4 x + 24) {D i s t r i b u t i o n p r o p e r t y}$
So, three multiplication expressions that can represent the product of the length and the width of the rectangle are
$\frac{1}{2} (4 x + 24), 2 (2 x + 6) a n d 4 (x + 3)$
Final Answer: $\frac{1}{2} (4 x + 24), 2 (2 x + 6) a n d 4 (x + 3)$

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