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Write as many expressions as you can that represent the area of this rectangle.
Large outer rectangle partitioned into 2 smaller rectangles, vertical side 10. First rectangle top side length 6. Second rectangle top side length 3 x.
In each row, write the equivalent expression. If you get stuck, use a diagram to organize your work. The first row is provided as an example. Diagrams are provided for the first three rows.
| factored | expanded |
|---|---|
Properties of operations can be used in different ways to rewrite expressions and create equivalent expressions. For example, the distributive property can be used to expand an expression such as
The distributive property can also be used in the other direction to factor an expression such as
The terms of the product go inside:
Think of a factor each term has in common:
Now think: "4 times what is 12x?" and "4 times what is -8?" Write the other factors on the other side of the rectangle:
So,
To expand an expression, use the distributive property to rewrite a product as a sum. The new expression is equivalent to the original expression.
For example, the expression
To factor an expression, use the distributive property to rewrite a sum as a product. The new expression is equivalent to the original expression.
For example, the expression
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