Area of a Rectangle: Opening parentheses

The area of a rectangle is equal to its length multiplied by the width.

We begin by writing the following exercise using the data shown in the figure:

$(3+2)\times(9+4)=$

We solve the exercise using the distributive property.

That is:

We multiply the first term of the left parenthesis by the first term of the right parenthesis.

We then multiply the first term of the left parenthesis by the second term of the right parenthesis.

Now we multiply the second term of the left parenthesis by the first term of the left parenthesis.

Finally, we multiply the second term of the left parenthesis by the second term of the right parenthesis.

In the following way:

$(3\times9)+(3\times4)+(2\times9)+(2\times4)=$

We solve each of the exercises within the parentheses:

$27+12+18+8=$

Lastly we solve the exercise from left to right:

$27+12=39$

$39+18=57$

$57+8=65$

The area of the rectangle is equal to the length multiplied by the width.

We begin by writing the exercise according to the existing data:

$7\times(4+5)$

We then solve the exercise by using the distributive property, that is, we multiply 7 by each of the terms inside of the parentheses:

$(7\times4)+(7\times5)=$

Lastly we solve the exercise inside of the parentheses and obtain the following:

$28+35=63$