Lesson 6, Topic 1
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### Multiplying out brackets:

To multiply out two binomial expressions such as (x + 3) (x + 3), make sure that each term in the second bracket is multiplied by each term in the first bracket.

(x + 3) (x + 3) = x(x + 3) + 3(x + 3)

= x2 + 3x + 3x + 9

= x2 + 6x + 9

Expand the brackets then simplify your expressions where possible.

This expansion can easily be remembered by the word FOIL.

F = First two terms

O = Outer two terms

I  =  Inner two terms

L = Last two terms

Using Foil Method

(x + 4)(x + 2)

Step 1: According to the FOIL Rule, the first step is to Multiply the First two terms, x, and x.

$$\scriptsize x \; \times \; x = x^2$$

Step 2: The second step is to Multiply the Outer terms, that is, x, and 2

$$\scriptsize x \; \times \; 2 = 2x$$

Step 3: The third step is to Multiply the Inner terms, that is, 4, and x

$$\scriptsize 4 \: \times \: x = 4x$$

Step 4: The fourth step is to Multiply the Last terms, that is, 4, and 2

$$\scriptsize 4 \: \times \: 2 = 8$$

= x2 + 2x + 4x + 8

= x2 + 6x + 8

Example 1

Expand the brackets then simplify your expression where possible.

a. (x + 5)(x + 2)

x(x + 2) + 5 (x + 2)

x2 + 2x + 5x  + 10

x2 + 7x  + 10

b. (x + 3)(x + 4)

= x(x + 4) + 3 (x + 4)

= x2 + 4x + 3x  + 12

= x2 + 7x  + 12

c. (a + 3) (a +5)

= a(a + 5 )  + 3( a + 5)

a2 + 5a + 3a + 15

a2 + 8a + 15

d. (x – 2)(x + 3)

= x(x + 3) – 2 (x + 3)

x2 + 3x – 2x  – 6

x2 + x  – 6

e. (2x – 5)(x + 3)

= 2x(x + 3) – 5(x + 3)

2x2 + 6x – 5x  – 15

2x2 + x  – 15

f. (3x – 2)(3x + 3)

= 3x(3x + 3) – 2(3x + 3)

9x2 + 9x – 6x  – 6

9x2 + 3x  – 6

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