## Expanding Double Brackets Using the Grid Method

Look at the grid below. It is a rectangle. It represents**(x + 1)(x + 2)**. Consider the

**entire rectangle**.

- The height of the entire rectangle is x + 1.
- The width of the entire rectangle is x + 2.
- The area of the rectangle is the
*height × width*. It is**(x + 1)(x + 2)**.

**dark blue rectangle**.

- The height of the dark blue rectangle is x.
- The width of the dark blue rectangle is x.
- The area of the dark blue rectangle is
**x**.^{2}

**light blue rectangle**.

- The height of the light blue rectangle is x.
- The width of the light blue rectangle is 2.
- The area of the light blue rectangle is
**2x**.

**orange rectangle**.

- The height of the orange rectangle is 1.
- The width of the orange rectangle is x.
- The area of the orange rectangle is
**x**.

**pink rectangle**.

- The height of the pink rectangle is 1.
- The width of the pink rectangle is 2.
- The area of the pink rectangle is
**2**.

(x + 1)(x + 2) = x

^{2}+ 2x + x + 2## A Real Example of How to Expand Double Brackets Using the Grid Method

Expanding brackets is easy. Expanding double brackets using the grid method is easy.## Question

Expand the brackets below.## Step-by-Step:

## 1

Find the

**first**term in the**first**brackets (x). Draw a vertical line and label its height with this term.## 2

Find the

**second**term in the**first**brackets (2). Draw a vertical line down from the vertical line already drawn. Label its height with this term.## 3

Find the

**first**term inside the**second**brackets (y). Draw a horizontal line from the vertical lines already drawn. Label its width with this term.## 4

Find the

**second**term inside the**second**brackets (3). Draw another horizontal line, following the horizontal line already drawn. Label its width with this term.## 5

Draw the rest of the grid.

## 6

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

## 7

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 (3).

x × 3 = 3x

## 8

Find the area of each rectangle in the grid by multiplying the height and width of each rectangle.
The area of the third grid is its height (2) times its width (y).

2 × y = 2y

## 9

Find the area of each rectangle in the grid by multiplying the height and width of each rectangle.
The area of the fourth grid is its height (2) times its width (3).

2 × 3 = 6

## 9

Add the areas of the rectangles in the grid.

xy + 3x + 2y + 6

## Answer:

Expanding**(x + 2)(y + 3)**gives

**xy + 3x + 2y + 6**.

## 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 = x

^{2}

## You might also like...

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