Expanding means removing the brackets and multiplying out the expressions. It is also called distributing.
To expand brackets means to multiply each term in the brackets by the term or expression outside the brackets. Equivalent expressions
Two brackets side by side
( )( ) mean you multiply them together.
Given expression = Expanded expression ( 4 )( 6 )
( 3 )( 7x) ( 4x)( 5x − 3 )
= = =
24 21x 20x2 –12x
Whatever is inside the brackets needs to be treated as a package. When multiplying: multiply the term on the outside by everything inside the brackets.
Multiplying an expression by a term: Term (expression)
Method 1: Multiply each inside term by the outside term
5x(2 x2 1 Expanded 10 x3
+ 4x − 7) + 20 x2
Method 2: Array method Create a rectangle with the expressions on diff erent sides of the rectangle.
− 35x 2
Find the area of each of the rectangles by multiplying the sides of each of the smaller rectangles. 2 x2
+4x 3
5x Add the areas from Step 2:
10 x3 +20 x2 − 7 − 35x 10 x3 + 20 x2
Worked example Expand the following and simplify if necessary. (i) 4(2x + 4y + 3)
Solution (i)
Recall the distributive property of numbers from Section A, Unit 4.