Distributing and Combining Like Terms in Algebra

The video tutorial covers the concepts of distributing and combining like terms in algebraic expressions. It begins with an introduction to these concepts and proceeds with multiple examples demonstrating how to apply the distributive property and combine like terms. The tutorial includes handling positive and negative terms, working with higher power terms, and understanding implicit multiplication. Each example is explained step-by-step to ensure clarity and understanding.

What are the two main steps involved in simplifying expressions that require both distributing and combining like terms?

• Only distribute

• First distribute, then combine like terms

• Only combine like terms

• First combine like terms, then distribute

When distributing a number outside the parentheses, what operation is performed?

• Addition

• Subtraction

• Multiplication

• Division

In the expression -4(8y + 4) - 3y, what is the result after distributing and combining like terms?

• -35y - 20

• -32y - 16

• -35y - 16

• -32y - 20

What is the first step when simplifying 6x + 2(7y + 8x)?

• Distribute 2 to both 7y and 8x

• Combine 6x and 2

• Subtract 2 from 6x

• Add 7y and 8x

After distributing and combining like terms in 6x + 2(7y + 8x), what is the simplified expression?

• 6x + 14y

• 22x + 16y

• 14y + 16x

• 22x + 14y

In the expression 6(-5y + 2y^2) + 8(7y^2 - 12), what is the result after distributing?

• 30y - 12y^2 + 56y^2 + 96

• -30y + 12y^2 + 56y^2 - 96

• -30y + 12y^2 + 56y^2 + 96

• 30y - 12y^2 + 56y^2 - 96

What is the combined result of the y^2 terms in the expression 6(-5y + 2y^2) + 8(7y^2 - 12)?

• 44y^2

• 68y^2

• 56y^2

• 12y^2

In the expression -5(-9y^4 + 8y) + 2(3y^4 - 5y), what is the result after distributing?

• 45y^4 + 40y + 6y^4 + 10y

• -45y^4 - 40y - 6y^4 - 10y

• 45y^4 - 40y + 6y^4 - 10y

• -45y^4 + 40y - 6y^4 + 10y

What is the combined result of the y^4 terms in the expression -5(-9y^4 + 8y) + 2(3y^4 - 5y)?

• 51y^4

• 6y^4

• 45y^4

• 39y^4

In the expression 2(5c + 3c^2) + 19c^2 + 4c, what is the simplified result?

• 22c^2 + 10c

• 22c^2 + 14c

• 25c^2 + 10c

• 25c^2 + 14c