Equivalent Expressions

Front

What is an equivalent expression?

Back

An equivalent expression is an expression that has the same value as another expression for all values of the variable(s) involved.

Front

How do you simplify the expression 10x - 16?

Back

You can factor out the common factor: 10x - 16 = 2(5x - 8).

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term in a binomial.

Front

How can you rewrite the expression 5(2x - 3) - 3x?

Back

Using the distributive property: 5(2x - 3) - 3x = 10x - 15 - 3x = 7x - 15.

Front

What is the process to combine like terms in the expression 3x + 4x + 6(x - 3) + 4?

Back

Combine like terms: 3x + 4x + 6x - 18 + 4 = 13x - 14.

Front

How do you apply the distributive property to the expression 3(2x + 8)?

Back

Distributing gives: 3(2x) + 3(8) = 6x + 24.

Front

What does it mean to factor an expression?

Back

Factoring an expression means rewriting it as a product of its factors, which can help simplify or solve equations.

Front

How can you factor the expression 18x - 9?

Back

You can factor out the greatest common factor: 18x - 9 = 9(2x - 1).

Front

What is the importance of equivalent expressions in algebra?

Back

Equivalent expressions allow for flexibility in solving equations and simplifying expressions, making it easier to work with them.

Front

What is a common mistake when simplifying expressions?

Back

A common mistake is failing to combine like terms correctly or misapplying the distributive property.