The LessonExpanding brackets means multiplying terms to remove brackets from an expression. Imagine we wanted to remove the brackets from the expression below. We have to expand the brackets.
How to Expand BracketsExpanding brackets is easy. Multiply each term inside the brackets with the term outside of the bracket.
QuestionExpand the brackets below.
Multiply the first term inside the brackets (x) with the term outside the brackets (2).
2 × x = 2x 2x
Multiply the second term inside the brackets (1) with the term outside the brackets (2), and add to the previous result.
2 × 1 = 2 2x + 2
Answer:Expanding 2(x + 1) gives 2x + 2.
A Formula to Expand BracketsThe formula below shows how to expand brackets:
a, b and c stand in for any number or term.
Lesson SlidesThe slider below shows another real example of how to expand brackets. In this example, there are more than two terms inside the brackets. Open the slider in a new tab
Multiplying a number with a variable
2 × x = 2x 5 × x = 5x
Multiplying a number with a variable with a coefficient
2 × 2x = 4x 3 × 5x = 15x
Multiplying a variable with a variable
x × y = xy x × x = x2
Be Careful with SignsEach term in the brackets will have a sign.
- positive terms have a + sign in front of them, or no sign if it is the first term.
- negative terms have a − sign in front of them.
Remember the rules for multiplying different signs: Same signs give a plus:
Different signs give a minus: