Expanding Brackets Using the Grid Method
(KS3, Year 7)
Expanding brackets means removing brackets from an expression. Imagine we wanted to remove the brackets from the expression below. We have to expand the brackets. 2 ( x plus 1 ) We can use the grid method to expand the brackets.

Expanding Brackets Using the Grid Method

Look at the grid below. It is a rectangle. It represents 2(x + 1). grid representing 2 ( x plus 1 ) Consider the entire rectangle. entire rectangle
  • The height of the entire rectangle is 2.
  • The width of the entire rectangle is x + 1.
  • The area of the rectangle is the height × width. It is 2(x + 1).
Now consider the two smaller rectangles that make up the entire rectangle. Consider the dark blue rectangle. dark rectangle
  • The height of the dark blue rectangle is 2.
  • The width of the dark blue rectangle is x.
  • The area of the dark blue rectangle is 2x.
Consider the light blue rectangle. light rectangle
  • The height of the light blue rectangle is 2.
  • The width of the light blue rectangle is 1.
  • The area of the light blue rectangle is 2.
The area of the dark blue rectangle and the light blue rectangle must add up to the area of the entire rectangle.
2(x + 1) = 2x + 2

A Real Example of How to Expand Brackets Using the Grid Method

Expanding single brackets using the grid method is easy.

Question

Expand the brackets below.
x ( y plus 2 )

Step-by-Step:

1

Find the term outside of the brackets (x). Draw a vertical line and label its height with this term. vertical line labelled x

2

Find the first term inside the brackets (y). Draw a horizontal line from the vertical line already drawn. Label its width with this term. horizontal line labelled y

3

Find the second term inside the brackets (2). Draw another horizontal line, following the horizontal line already drawn. Label its width with this term. horizontal line labelled 2

4

Draw the rest of the grid. grid

5

Find the area of each rectangle in the grid by multiplying the height and width of each rectangle. The area of the first grid is its height (x) times its width (y).
x × y = xy
x times y equals xy

6

Find the area of each rectangle in the grid by multiplying the height and width of each rectangle. The area of the second grid is its height (x) times its width (2).
x × 2 = 2x
x times 2 equals 2x

7

Add the areas of the rectangles in the grid.
xy + 2y

Answer:

Expanding x(y + 2) gives xy + 2x.

Lesson Slides

The slider below shows another real example of how to expand single brackets using the grid method. In this example, there are more than two terms inside the brackets.

Multiplication Tips

  • 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

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This page was written by Stephen Clarke.