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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 to get .
The distributive property can also be used in the other direction to factor an expression such as . In this case, we know the product and need to find the factors.
The terms of the product go inside:
Think of a factor each term has in common: and each have a factor of 4. The common factor can be placed on one side of the large rectangle:
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, is equivalent to .
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 can be expanded to get the equivalent 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 can be factored to get the equivalent expression .