Simplifying Expressions and Terms

In this video, Mr. Tarrou explains how to simplify algebraic expressions by combining like terms. He begins by defining expressions and like terms, emphasizing the importance of matching variables and exponents. Through various examples, he demonstrates how to identify and combine like terms, including the use of the distributive property. The video also covers more complex examples involving fractions, providing a comprehensive guide to simplifying expressions in algebra.

What is a key characteristic of like terms in an expression?

• They have the same variables raised to the same power.

• They have the same variables raised to different powers.

• They are always constants.

• They have different variables.

Which of the following is considered a term in an expression?

• A variable alone

• A product of a number and a variable

• All of the above

• A number alone

How are terms in an expression typically separated?

• By multiplication and division

• By parentheses

• By exponents

• By addition and subtraction

In the expression 4b - b, what is the simplified form?

• b

• 5b

• 3b

• 2b

When rearranging terms in an expression, what must be kept with each term?

• The exponent

• The sign

• The variable

• The coefficient

What happens when you multiply a negative number by a positive number?

• The result is undefined

• The result is zero

• The result is negative

• The result is positive

In the expression -3y - (4y + 3x), what is the simplified form?

• -3y + 4y - 3x

• -3y - 4y + 3x

• -7y + 3x

• -7y - 3x

What is the result of combining -3x and 4x?

• 1x

• -1x

• 7x

• -7x

When dealing with fractions in expressions, what is necessary for combining like terms?

• Common denominators

• Different denominators

• No denominators

• Negative denominators

In the expression 1/2(2x^2 - y^2) - 4/3(x^2 + y^2), what is the simplified form?

• 1/3x^2 - 11/6y^2

• -1/3x^2 - 11/6y^2

• -1/3x^2 + 11/6y^2

• 1/3x^2 + 11/6y^2