Topic Content:
- Multiplying Out two Binomial Expressions
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
Example:
Solve the expression below 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
Worked Example 6.6.1:
Expand the brackets then simplify your expression where possible.
a. (x + 5)(x + 2)
b. (x + 3)(x + 4)
c. (a + 3) (a +5)
d. (x – 2)(x + 3)
e. (2x – 5)(x + 3)
f. (3x – 2)(3x + 3)
Solution
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