Simplifying Equations with Factoring

Let's rewrite this expression by distributing the three. We multiply the three by each term inside the parenthesis. 3 * a is 3 a. 3 * 2 b is 6 b. Our expression is 3 a + 6 b. Now let's work in reverse. This is called factoring. We'll take 3 a + 6 b and get back to the original form. We can factor out a 3, which means we divide each term by 3. 3 a / 3 is a. 6 b / 3 is 2 b. To factor an expression, we look for a common factor in all terms. Here, both 3 a and 6b can be divided by 3. We can then pull the common factor outside of the parenthesis. What's left inside the parenthesis is each original term divided by that factor.

Let's practice factoring another expression. Here we have 5 a minus 15.

We divide each term by five. 5 a / 5 is a 15 / 5 is 3. Our factored expression is 5 * the quantity a - 3.

Here's another 10 b + 15 c. First, we find the greatest common factor of both terms. The largest number that divides into both 10 and 15 is five. We place 5 outside the parenthesis. 10 B / 5 gives us 2 B and 15 C / 5 is 3 C. Our factored expression is 5 * the quantity 2 B + 3 C.

Let's try one more. We need to factor 4 Y + 12 Z. The greatest common factor of 4 and 12 is 4. So let's factor out four.

4 y / 4 leaves us with y. 12 z / 4 gives us 3 z. Our factored expression is 4 * the quantity y + 3 z. Factoring is the reverse of distributing. It's rewriting an expression by pulling out the greatest common factor. This helps us organize terms, which is often a first step in simplifying expressions or solving equations.