Simplifying Algebraic Expressions

The video tutorial explains how to simplify algebraic expressions by combining like terms. It begins with an introduction to like terms, which are terms with the same variable factors and exponents, including constant terms. The tutorial provides three examples: simplifying 5x + 8 + 4x + 7, 6y² + 12y + y², and 4z² + 4z + 2. Each example demonstrates the process of identifying like terms, rearranging them, and combining their coefficients to simplify the expression. The tutorial emphasizes the importance of writing terms in descending order based on exponents.

What is the first step in simplifying expressions?

• Multiply all terms

• Combine like terms

• Divide by the highest coefficient

• Subtract constant terms

In the expression 5x + 8 + 4x + 7, which terms are considered like terms?

• 5x and 8

• 4x and 7

• 5x and 4x

• 8 and 4x

What is the simplified form of the expression 5x + 8 + 4x + 7?

• 5x + 4x + 15

• 9x + 8

• 5x + 4x + 7

• 9x + 15

In the expression 6y^2 + 12y + y^2 - 3y, what is the coefficient of y^2?

• 3

• 12

• 1

• 6

What is the simplified form of the expression 6y^2 + 12y + y^2 - 3y?

• 6y^2 + 9y

• 7y^2 + 9y

• 6y^2 + 12y

• 7y^2 + 12y

In the expression 4z^2 + 4z + 2 - z^2 + 5 - 4z + 2z^3, which term has no like terms?

• 4z^2

• 2z^3

• 4z

• 5

What is the simplified form of the expression 4z^2 + 4z + 2 - z^2 + 5 - 4z + 2z^3?

• 2z^3 + 4z + 7

• 2z^3 + 3z^2 + 7

• 2z^3 + 4z^2 + 7

• 3z^2 + 4z + 7

What is the result of combining the z terms in the expression 4z - 4z?

• 1z

• 8z

• 0

• 4z

What is the sum of the constant terms 2 and 5 in the expression?

• 9

• 7

• 2

• 5

What is the final simplified expression in the tutorial?

• 3z^2 + 2z^3

• 2z^3 + 7

• 3z^2 + 7

• 2z^3 + 3z^2 + 7