Combining Like Terms and Distributing

The video tutorial covers three main algebraic concepts: distributing terms in expressions, combining like terms with different variables, and distributing negative signs across grouped terms. It provides step-by-step explanations and encourages solving problems mentally without writing intermediate steps. The tutorial emphasizes the importance of recognizing negative signs as part of terms and how to handle them when combining terms.

What is the first step in distributing 3a across the terms in the expression 3a * a + 4a^2?

• Multiply 3a by a

• Add 3a to 4a^2

• Subtract 3a from 4a^2

• Divide 3a by a

After distributing 3a across the terms, what is the intermediate expression?

• 3a^2 + 12a^3

• 3a + 4a^2

• 3a^2 + 4a^2

• 3a^2 + 3a * 4a^2

What is the final simplified result of the expression 3a * a + 3a * 4a^2?

• 3a^2 + 12a^2

• 12a^3 + 4a^2

• 3a^2 + 12a^3

• 3a^2 + 4a^2

When combining like terms, which terms are considered x terms?

• 3x and 6x

• -2y and -8y

• 3x and -2y

• 6x and -8y

What is the result of combining the x terms 3x and 6x?

• 0

• 6x

• 3x

• 9x

What is the result of combining the y terms -2y and -8y?

• 10y

• 6y

• -10y

• -6y

What is the first step in subtracting terms in the expression 4a + 3b - (2a + 5b)?

• Distribute the negative sign

• Add 2a and 5b

• Multiply 4a by 2a

• Divide 3b by 5b

How does the term -5b change when the negative sign is distributed?

• It becomes +5b

• It becomes -10b

• It remains -5b

• It becomes 0

What happens to the sign of each term in a group when a negative sign is distributed across it?

• The terms remain unchanged

• The sign of each term is reversed

• The terms are added together

• The terms are multiplied by 2

In the expression 4a + 3b - (2a + 5b), what is the equivalent expression after distributing the negative sign?

• 4a - 3b - 2a + 5b

• 4a - 3b + 2a - 5b

• 4a + 3b + 2a + 5b

• 4a + 3b - 2a - 5b