Expanding double brackets: FOIL and multiplication grid

​​In a nutshell

To expand double brackets, multiply each term in the first bracket with each term in the second bracket using the FOIL method and then simplify. You can also use a multiplication grid. 

FOIL method

The FOIL method stands for First Outside Inside Last. This makes sure that you multiply all terms together and is a good checklist to follow when expanding double brackets.

PROCEDURE

Example 1

Expand the following double brackets.

$$(x + 2)(x + 3)$$

Using FOIL, we first multiply the first terms of both brackets (F).

$$x \times x = x^2$$​ 

​Then multiply the first term in the first bracket by the second term in the second bracket (O).

$$x \times 3 = 3x$$​​

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Then multiply the second term in the first bracket by the first term in the second bracket (I).

$$2 \times x = 2x$$

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Then multiply the second term in both brackets together (L).

$$3 \times 2 = 6$$

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Then add all the products together and simplify.

$$x^2 + 2x + 3x + 6 = \underline {x^2 + 5x + 6}$$

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Example 2

Expand the following double brackets.

$$(4x - 3)(5x + 5)$$

Using FOIL, we first multiply the first terms of both brackets (F).

$$4x \times 5x = 20x^2$$​​

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Then multiply the first term in the first bracket by the second term in the second bracket (O).

$$4x \times 5 = 20x$$

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Then multiply the second term in the first bracket by the first term in the second bracket (I).

​$$-3 \times 5x = -15x$$

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Then multiply the second term in both brackets together (L).

$$-3 \times 5 = -15$$

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Then add all the products together and simplify.

$$20x^2 + 20x - 15x -15 = \underline {20x^2 + 5x - 15}$$

Multiplication grid

When using a multiplication grid put the two terms from one bracket at the top and the two terms from the other bracket on the left side leaving space between for your products. Then add all products in the grid together to get your final answer.

Example 3

Expand the following double brackets.

​$$(x+5)(x+9)$$​

​$$\begin {array} {c|c:c} & x & +5 \\ \hline x & x^2 & +5x \\ \hdashline+9 & +9x & +45\end {array}$$

Now add the products and simplify.

$$x^2 + 5x + 9x +45 = \underline {x^2 +14x + 45}$$

Example 4

Expand the following double brackets.

$$(x-2)(x+8)$$​​

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$$\begin {array} {c|c:c} & x & -2 \\ \hline x & x^2 & -2x \\ \hdashline+8 & +8x & -16\end {array}$$​​

Now add the products and simplify.

$$x^2 -2x +8x -16 = \underline {x^2 +6x -16}$$​​