Question

the
ew look\ of the cereal boxes has a length that is three more than two times the width, x, and a height that is one more than four times the width. write expressions for the dimensions, then complete the statements.
the expression for the volume of the boxes is
done

Explanation:

Step1: Define width, length, height

Width: $w = x$
Length: $l = 2x + 3$
Height: $h = 4x + 1$

Step2: Apply volume formula

Volume $V = l \times w \times h$
$V = (2x+3) \times x \times (4x+1)$

Step3: Multiply first two terms

$V = x(2x+3)(4x+1) = (2x^2+3x)(4x+1)$

Step4: Expand the product

$V = 2x^2(4x) + 2x^2(1) + 3x(4x) + 3x(1)$
$V = 8x^3 + 2x^2 + 12x^2 + 3x$

Step5: Combine like terms

$V = 8x^3 + (2x^2+12x^2) + 3x$
$V = 8x^3 + 14x^2 + 3x$

Answer:

$8x^3 + 14x^2 + 3x$