Simplifying and Factoring Expressions

Front

What is the distributive property in algebra?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

Front

How do you simplify the expression 3(9a + 2) + 5(2a - 4)?

Back

First, apply the distributive property: 3*9a + 3*2 + 5*2a - 5*4 = 27a + 6 + 10a - 20. Combine like terms to get 37a - 14.

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

What is the factored form of -8x - 10?

Back

-2(4x + 5) is the factored form of -8x - 10.

Front

How do you simplify the expression -6x + 4(-x - 3)?

Back

Distribute 4: -6x + 4*-x + 4*-3 = -6x - 4x - 12. Combine like terms to get -10x - 12.

Front

What is a constant in algebra?

Back

A constant is a fixed value that does not change and is not multiplied by a variable.

Front

What is the factored form of 12x - 20?

Back

4(3x - 5) is the factored form of 12x - 20.

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power, allowing them to be combined.

Front

How do you combine like terms in an expression?

Back

To combine like terms, add or subtract the coefficients of the terms that have the same variable.

Front

What is the first step in simplifying an expression?

Back

The first step is to apply the distributive property if there are parentheses in the expression.