Combining Like Terms and Simplifying Expressions

The video tutorial explains how to identify and combine like terms in algebraic expressions. It covers the concept of like terms, which are terms with the same variable factors and exponents. The tutorial demonstrates combining like terms by adding or subtracting their coefficients while keeping the variable part unchanged. Examples include expressions with variables v, x, c, and d, as well as terms with fractional coefficients. The video emphasizes the importance of simplifying expressions by combining like terms and provides step-by-step guidance for each example.

What are like terms?

• Terms with different exponents

• Terms with the same coefficients

• Terms with the same variable factors and exponents

• Terms with different variables

In the expression 3v + 7v - v + v, what is the combined coefficient of v?

• 11

• 9

• 10

• 8

How do you treat the term '-v' when combining like terms?

• As 1v

• As -1v

• As -2v

• As 0v

In the expression x + 6x^2 + 8x + x^3 - x^2, which term should be written first when simplifying?

• 8x

• x^3

• 6x^2

• x

What is the simplified form of the expression x + 6x^2 + 8x + x^3 - x^2?

• x^3 + 7x^2 + 8x

• x^3 + 5x^2 + 9x

• x^3 + 5x^2 + 13x

• x^3 + 6x^2 + 8x

In the expression 5c + 2d + c - (-3d), what is the simplified form?

• 6c + 5d

• 5c + 2d

• 6c + 2d

• 5c + 5d

How do you handle the term '-(-3d)' in the expression 5c + 2d + c - (-3d)?

• As -3d

• As 2d

• As +3d

• As 0d

In the expression 1/2y - 3/7y + y, what is the common denominator used to combine the terms?

• 28

• 21

• 14

• 7

What is the simplified form of the expression 1/2y - 3/7y + y?

• 15/14y

• 14/15y

• 1/14y

• 1/2y

When combining like terms with fractions, what is the first step?

• Subtract the numerators

• Multiply the fractions

• Add the numerators directly

• Find a common denominator