Comparing Rectangle Areas: 30x×(4x+8) vs (7+27x)×5 in Fabric Production

In a fabric factory, the possible sizes of fabric are:

$30x\times(4x+8)$

$(7+27x)\times5$

How much more material does the factory need?

We begin by simplifying the two exercises using the distributive property:

We start with the first expression.

$30x\times(4x+8)=$

$30x\times4x+30x\times8=$

$120x^2+240x$

We now address the second expression:

$(7+27x)\times5=$

$5\times7+5\times27x=$

$35+135x$

In order to calculate the expressions, let's assume that in each expression x is equal to 1.

We can now substitute the X value into the equation:

$120x^2+240x=120\times1^2+240\times1=120+240=360$

$35+135\times1=35+135=170$

Hence it seems that the first expression is larger and requires more fabric.

Let's now calculate the expressions assuming that x is less than 1. We substitute this value into each of the expressions as follows:$x=\frac{1}{10}$

$\frac{120}{100}+\frac{240}{10}=1\frac{1}{5}+24=25\frac{1}{5}$

$35+\frac{135}{10}=48.5$

This time the second expression seems to be larger and requires more fabric.

Therefore, it is impossible to determine.