Expand and Factor Expressions

Front

What is the greatest common factor (GCF)?

Back

The greatest common factor (GCF) is the largest positive integer that divides all the given numbers without leaving a remainder.

Front

How do you find the GCF of two numbers?

Back

To find the GCF of two numbers, list the factors of each number and identify the largest factor that appears in both lists.

Front

What is the GCF of 20 and 36?

Back

The GCF of 20 and 36 is 4.

Front

What does it mean to factor an expression?

Back

Factoring an expression means rewriting it as a product of its factors.

Front

How do you factor the expression 18x + 24y?

Back

To factor 18x + 24y, find the GCF, which is 6, and rewrite the expression as 6(3x + 4y).

Front

What is the distributive property?

Back

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

Front

Use the distributive property to expand 4(a + 3b). What is the result?

Back

The result is 4a + 12b.

Front

What is an equivalent expression?

Back

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

Front

Which expression is equivalent to (1/5)(15 + 10x - 5)?

Back

The expression equivalent to (1/5)(15 + 10x - 5) is 2 + 2x.

Front

What is the process of expanding an expression?

Back

Expanding an expression involves distributing factors and combining like terms to rewrite it in a simplified form.