Suppose you multiplied the cereal box dimensions in a different order: [tex]V=(x)(4 x+3)(4 x)[/tex]

First, [tex](x)(4 x+3)=[/tex] ?

Multiply x by each term inside the parentheses ( 4 x + 3 ) .
x × 4 x = 4 x 2 .
x × 3 = 3 x .
Combine the terms: 4 x 2 + 3 x ​ .

Explanation

Understanding the problem We are asked to find the product of ( x ) and ( 4 x + 3 ) . This involves using the distributive property to multiply the term x by each term inside the parentheses.

Applying the distributive property To multiply ( x ) ( 4 x + 3 ) , we distribute x to both terms inside the parentheses:


x ( 4 x + 3 ) = x ( 4 x ) + x ( 3 )

Simplifying the expression Now, we perform each multiplication separately:

x ( 4 x ) = 4 x 2 x ( 3 ) = 3 x
So, x ( 4 x + 3 ) = 4 x 2 + 3 x

Final result Therefore, the result of multiplying ( x ) and ( 4 x + 3 ) is 4 x 2 + 3 x .

Examples
Understanding how to multiply expressions like ( x ) ( 4 x + 3 ) is fundamental in many areas. For example, if you're designing a rectangular garden where the width is x meters and the length is 4 x + 3 meters, then the area of the garden is given by the expression x ( 4 x + 3 ) = 4 x 2 + 3 x square meters. Knowing how to expand this expression allows you to calculate the area for different values of x and optimize your garden design.

Answered by GinnyAnswer | 2025-07-07