Pre-Algebra Examples

 $\begin{array}{r} h = & x \\ l = & 36 - 2 x \\ w = & x \end{array}$

Step 1

The surface area of a box is equal to the sum of the areas of each side of the box.

$2 \cdot (l e n g t h) \cdot (w i d t h) + 2 \cdot (l e n g t h) \cdot (h e i g h t) + 2 \cdot (w i d t h) \cdot (h e i g h t)$

Step 2

Substitute the values of the length $l = 36 - 2$ , the width $w = x$ , and the height $h = x$ into the formula.

$2 \cdot 36 - 2 \cdot x + 2 \cdot 36 - 2 \cdot x + 2 \cdot x \cdot x$

Step 3

Simplify each term.

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Step 3.1

Multiply $2$ by $36$ .

$72 - 2 \cdot x + 2 \cdot 36 - 2 \cdot x + 2 \cdot x \cdot x$

Step 3.2

Multiply $2$ by $36$ .

$72 - 2 x + 72 - 2 \cdot x + 2 \cdot x \cdot x$

Step 3.3

Multiply $x$ by $x$ by adding the exponents.

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Step 3.3.1

Move $x$ .

$72 - 2 x + 72 - 2 x + 2 \cdot (x \cdot x)$

Step 3.3.2

Multiply $x$ by $x$ .

$72 - 2 x + 72 - 2 x + 2 \cdot x^{2}$

$72 - 2 x + 72 - 2 x + 2 x^{2}$

Step 4

Simplify by adding terms.

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Step 4.1

Add $72$ and $72$ .

$- 2 x + 144 - 2 x + 2 x^{2}$

Step 4.2

Subtract $2 x$ from $- 2 x$ .

$- 4 x + 144 + 2 x^{2}$

$- 4 x + 144 + 2 x^{2} x^{2}$