How to simplify a big expression by combining like terms | Algebra I | Khan Academy | Summary and Q&A

TL;DR

Simplify the given algebraic expression by combining like terms and following common sense intuition.

Key Insights

• 😑 Simplifying algebraic expressions involves combining like terms and following common sense intuition.
• 😑 Coefficients represent the numbers multiplied by variables in an expression.
• 😑 It is important to add or subtract the same terms when simplifying expressions.

Transcript

We have a hairy-looking expression here. And your goal is to try to simplify it as much as you can. And I'll give you a little bit of time to do it. Let's just think about it, step by step. And it might help if we were to actually reorder the terms in this expression. So let me put all the x terms first. So I have 5x-- that's that term-- minus 2x. ... Read More

Questions & Answers

Q: How can we simplify the given algebraic expression?

To simplify the expression, we need to rearrange the terms and combine like terms. Start by combining the x terms, then the y terms, the z terms, and finally the constant term.

Q: What is a coefficient in algebraic expressions?

A coefficient is the number multiplied by a variable. In this expression, the coefficients are 5, -2, 7, 3, 8, -1, and 1 (implicit).

Q: Why is it important to add and subtract the same terms in algebraic expressions?

Adding and subtracting the same terms ensures that we are manipulating the same variables. In this case, we add/subtract x's, y's, and z's separately because they represent different variables.

Q: Can we simplify the expression by merging x's, y's, and z's?

No, we cannot merge x's, y's, and z's together in a simple way because they represent different variables. Each variable needs to be combined separately.

Summary & Key Takeaways

• The given expression is simplified by rearranging the terms and combining like terms.

• Like terms with x are combined to get 3x, like terms with y are combined to get 10y, and like terms with z are combined to get 7z.

• The expression simplifies to 3x + 10y + 7z + 5.