How to simplify an expression by combining like terms and the distributive property | Khan Academy | Summary and Q&A

TL;DR

Learn how to simplify expressions using the distributive property by distributing coefficients and combining like terms.

Key Insights

• 😑 Simplifying expressions using the distributive property involves distributing coefficients to each term inside parentheses.
• 🍉 Combining like terms in an expression simplifies it further by adding or subtracting the coefficients of similar terms.
• 😑 The distributive property is a fundamental concept in mathematics and is directly applicable to simplifying algebraic expressions.
• 💨 Simplification involves applying familiar arithmetic principles in a systematic way.
• 😑 Breaking down an expression into smaller parts makes it easier to simplify.
• 🤘 Distributing a negative coefficient can involve changing the signs of the terms being distributed.
• 😑 Simplifying expressions with multiple terms requires careful handling of coefficients and signs.

Transcript

I've gotten feedback that all the Chuck Norris imagery in the last video might have been a little bit too overwhelming. So for this video, I've included something a little bit more soothing. Let's try to simplify some more expressions. And we'll see we're just applying ideas that we already knew about. Let's say I want to simplify the expression 2 ... Read More

Questions & Answers

Q: What does it mean to simplify an expression using the distributive property?

Simplifying an expression using the distributive property involves multiplying the coefficient outside the parentheses to each term inside the parentheses and then combining like terms.

Q: Can you explain how to simplify the expression 2 times 3x plus 5?

To simplify 2 times 3x plus 5, distribute the coefficient of 2 to both terms inside the parentheses: 2 times 3x is 6x, and 2 times 5 is 10. The expression simplifies to 6x plus 10.

Q: How do you simplify an expression with multiple terms, like 7 times 3y minus 5 minus 2 times 10 plus 4y?

Start by distributing the coefficient of 7 to the terms inside the parentheses: 7 times 3y is 21y, and 7 times -5 is -35. Then, distribute the coefficient of -2 to the terms after the minus sign: -2 times 10 is -20, and -2 times 4y is -8y. Finally, combine the like terms: 21y minus 8y simplifies to 13y, and -35 minus 20 simplifies to -55. The expression simplifies to 13y minus 55.

Q: How do you know which terms to combine when simplifying an expression?

To combine terms, look for like terms that have the same variable and exponent. In the expression 13y minus 55, the two terms both have y as the variable, so you can combine them. However, you cannot combine the terms with different variables or exponents.

Summary & Key Takeaways

• To simplify an expression like 2 times 3x plus 5, you can distribute the coefficient of 2 and simplify to 6x plus 10.

• When dealing with multiple terms in an expression, distribute each coefficient separately and then combine like terms.

• For example, simplifying 7 times 3y minus 5 minus 2 times 10 plus 4y involves distributing the coefficients and combining like terms, resulting in 13y minus 55.