Expand, factor, and combine linear expressions · lesson

Combining like terms

💡 Add the coefficients of the x terms, and add the plain numbers, keeping each sign with its term.

Like terms have the same letter part. Add their coefficients. A lone x has a coefficient of 1.

Keep each sign with the term after it. In 7x − 3, the 3 is really −3.

Decimals and negatives combine the same way.

🧠 Let's work it out

Simplify −5x + 4 + 2x − 9.

What do you think comes next?

💡 Multiply the outside number, sign and all, by every term inside.

The outside number multiplies each term inside the parentheses. Its sign goes with it.

A negative times a negative is positive. So −3 times −5 is +15.

A fraction outside works the same way. (1/3)(9x) is 3x.

🧠 Let's work it out

Multiply out −3(2x − 5).

What do you think comes next?

💡 A minus sign in front of parentheses changes the sign of every term inside.

Subtracting a group means subtracting each term in it. Think of the minus as −1 times the group.

So −(4x − 5) becomes −4x + 5. Both signs flip.

🧠 Let's work it out

Find (6x + 1) − (4x − 5).

What do you think comes next?

💡 Clear every set of parentheses first, watching the signs, then combine like terms.

When an expression has parentheses and other terms, expand first. Then combine.

If a negative number sits in front of the parentheses, it multiplies every term inside.

🧠 Let's work it out

Simplify 5(x + 1) − 2(x − 3).

What do you think comes next?

💡 To factor, pull out the greatest common factor and divide each term by it.

Factoring writes an expression as a product. Find the greatest common factor (GCF) of the numbers.

Put the GCF outside. Inside, write each term divided by the GCF. Keep the signs.

Check by multiplying back out.

🧠 Let's work it out

Factor 12x − 18.

What do you think comes next?