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Simplifying Expressions and Combining Like Terms - Problem 2

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

When simplifying an algebraic expression that involves a number outside some parentheses, start by distributing. Distributing (or the distributive property) means that if a quantity, which is a group of terms inside parentheses, is being multiplied by a number outside the parentheses, then all the terms inside the parentheses need to be multiplied by that number. In other words, that number is being distributed to all the terms inside the parentheses. Once the number has been distributed, then continue to simplify by adding like terms. Remember that like terms are terms with the same variable raised to the same exponent or power. Combine like terms by combining the coefficient and leaving the variable form the same.

This is a problem where I'm asked to simplify an expression. In my head I'm thinking about okay simplify, that probably means combining like terms. But before I see any like terms here I need to do what's called distributing. Distributing is a form of multiplication where I'm reading this problem it means 3 times the quantity x minus 1 plus 4x. That means the 3 has to get multiplied by the x and also by the -1. That's called distributing or the distributive property.

Once I've done the distributing now I'm ready to simplify by combining like terms. I have Xs that are raised to a singular power so I have 3x plus 4x is 7x, don't forget that take away 3 and that's my most simplified form.

So when you guys come to problems like these that have q number outside of some parentheses use the distributive property where that number outside gets multiplied by both of the quantities inside the parentheses. And be really careful with the minus signs also because that's where a lot of students make their mistakes.

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