In this lesson, students have an opportunity to demonstrate fluency in combining like terms and look for and make use of structure (MP7) to apply the distributive property in more sophisticated ways.
- Explain (orally and in writing) how to write an equivalent expression with fewer terms.
- Generalize (orally) about what strategies are useful and what mistakes are common when writing equivalent expressions with fewer terms.
- Identify equivalent expressions, and justify (orally and in writing) that they are equivalent.
Let’s see how we can combine terms in an expression to write it with less terms.
- Given an expression, I can use various strategies to write an equivalent expression.
- When I look at an expression, I can notice if some parts have common factors and make the expression shorter by combining those parts.
To expand an expression, we use the distributive property to rewrite a product as a sum. The new expression is equivalent to the original expression.
For example, we can expand the expression \(5(4x+7)\) to get the equivalent expression \(20x + 35\).
factor (an expression)
To factor an expression, we use the distributive property to rewrite a sum as a product. The new expression is equivalent to the original expression.
For example, we can factor the expression \(20x + 35\) to get the equivalent expression \(5(4x+7)\).
A term is a part of an expression. It can be a single number, a variable, or a number and a variable that are multiplied together. For example, the expression \(5x + 18\) has two terms. The first term is \(5x\) and the second term is 18.