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JSS1: MATHEMATICS - 2ND TERM

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  1. Algebraic Processes | Week 1
    4 Topics
    |
    1 Quiz
  2. Simplification of Algebraic Expressions | Week 2
    4 Topics
    |
    1 Quiz
  3. Simplification of Algebraic Expressions 2 (Use of Brackets) | Week 3
    4 Topics
    |
    1 Quiz
  4. Simple Equations | Week 4
    1 Topic
    |
    1 Quiz
  5. Simple Equations II | Week 5
    3 Topics
    |
    1 Quiz
  6. Plane Shapes I | Week 6
    5 Topics
    |
    2 Quizzes
  7. Plane Shapes II | Week 7
    7 Topics
    |
    1 Quiz
  8. Plane Shapes III | Week 8
    7 Topics
    |
    1 Quiz
  9. Decimal and Percentages I | Week 9
    2 Topics
    |
    1 Quiz
  10. Decimal and Percentages | Week 10
    3 Topics
    |
    1 Quiz



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To expand a bracket means to multiply each term in the bracket by the expression outside the bracket.

For example:  a(x  +  y)  means \( \scriptsize a \: \times \: x \: + \: a \; \times \: y \\ = \scriptsize ax \: + \: ay \)

Also a(x –  y )  =   \( \scriptsize a \; \times \; x \; – \; a \; \times \; y \\ = \scriptsize ax \; – \; ay \)

The equation can also be written like this

(x   +   y) a  =   xa   +   ya  

(x   –  y) a   =   xa   –  ya

Example:

Expand the brackets in the following:

i. \( \scriptsize 5(x \: + \: y) \)
ii. \( \scriptsize 3(x \: + \: 2y) \)
iii. \( \scriptsize 10(p \; – \: q \; – \: r) \)
iv. \( \scriptsize – (3y \; – \: 4z) \)
v. \( \scriptsize 3a \: + \: (4y \; – \: 2a) \)

Solution:

i. \( \scriptsize 5(x \: + \: y) \)

= \( \scriptsize 5 \: \times \: x \: + \: 5 \: \times \: y \\ = \scriptsize 5x \: + \: 5y \)

ii. \( \scriptsize 3(x \: + \: 2y) \)

\( \scriptsize = 3 \: \times \: x \: + \: 3 \: \times \: 2y \)

\( \scriptsize= 3x \: + \: 6y \)

iii. \( \scriptsize 10(p \; – \: q \; – \: r) \)

\( \scriptsize = 10 \: \times \: p \; – \: 10 \: \times \: q \; – \: 10 \: \times \: r \)

\( \scriptsize = 10p \; – \: 10q \; – \: 10r \)

iv. \( \scriptsize – (3y \; – \: 4z) \)

Open the brackets

Note: \( \scriptsize – \: \times \: – \: = + \)

\( \scriptsize = 3y \: + \: 4z \)

v. \( \scriptsize 3a \: + \: (4y \; – \: 2a) \)

Open the brackets

= \( \scriptsize 3a \: + \: 4y \; – \: 2a \)

Collect like terms

= \( \scriptsize 3a \; – \: 2a \: + \: 4y \)

= \( \scriptsize a \: + \: 4y \)

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