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JSS3: MATHEMATICS - 1ST TERM

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  1. Binary Number System I | Week 1
    5 Topics
    |
    1 Quiz
  2. Binary Number System II | Week 2
    6 Topics
    |
    1 Quiz
  3. Word Problems I | Week 3
    4 Topics
    |
    1 Quiz
  4. Word Problems with Fractions II | Week 4
    1 Topic
    |
    1 Quiz
  5. Factorization I | Week 5
    4 Topics
    |
    1 Quiz
  6. Factorization II | Week 6
    3 Topics
    |
    1 Quiz
  7. Factorization III | Week 7
    3 Topics
    |
    1 Quiz
  8. Substitution & Change of Subject of Formulae | Week 8
    2 Topics
    |
    1 Quiz
  9. Simple Equations Involving Fractions | Week 9
    3 Topics
    |
    1 Quiz
  10. Word Problems | Week 10
    1 Topic
    |
    1 Quiz



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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.

\( \scriptsize x \; \times \; x = x^2 \)

Screenshot 2023 08 22 at 11.42.20

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

\( \scriptsize x \; \times \; 2 = 2x \)

Screenshot 2023 08 22 at 11.42.02

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

\( \scriptsize 4 \: \times \: x = 4x \)

Screenshot 2023 08 22 at 11.41.42

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

\( \scriptsize 4 \: \times \: 2 = 8\)

Screenshot 2023 08 22 at 11.41.22
Screenshot 2023 08 23 at 07.21.30

= 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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