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 combine like terms in an expression?

Back

To combine like terms, identify terms that have the same variable raised to the same power and add or subtract their coefficients.

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 inside a parenthesis.

Front

How can you simplify the expression 15x + 10 - 6x - 1?

Back

Combine like terms: (15x - 6x) + (10 - 1) = 9x + 9.

Front

What is the result of applying the distributive property to 6(3y - 2y + 7)?

Back

6(3y - 2y + 7) simplifies to 6y + 42.

Front

How do you rearrange the expression z + z^2 + 1?

Back

You can rearrange it to 1 + z + z^2, as addition is commutative.

Front

What is the result of distributing 7 in the expression 7(3a + 4b)?

Back

Distributing gives 21a + 28b.

Front

How do you simplify the expression 6y + 22y + y?

Back

Combine like terms: 6y + 22y + y = 29y.

Front

What is the importance of equivalent expressions in algebra?

Back

Equivalent expressions allow for flexibility in solving equations and simplifying problems, making it easier to find solutions.

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 equations.