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JSS2: MATHEMATICS - 2ND TERM

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  1. Transactions in the Homes and Offices | Week 1
    5 Topics
    |
    1 Quiz
  2. Expansion and Factorization of Algebraic Expressions | Week 2
    4 Topics
    |
    1 Quiz
  3. Algebraic Expansion and Factorization of Algebraic Expression | Week 3
    4 Topics
    |
    1 Quiz
  4. Algebraic Fractions I | Week 4
    4 Topics
    |
    1 Quiz
  5. Addition and Subtraction of Algebraic Fractions | Week 5
    2 Topics
    |
    1 Quiz
  6. Solving Simple Equations | Week 6
    4 Topics
    |
    1 Quiz
  7. Linear Inequalities I | Week 7
    4 Topics
    |
    1 Quiz
  8. Linear Inequalities II | Week 8
    2 Topics
    |
    1 Quiz
  9. Quadrilaterals | Week 9
    2 Topics
    |
    1 Quiz
  10. Angles in a Polygon | Week 10
    4 Topics
    |
    1 Quiz
  11. The Cartesian Plane Co-ordinate System I | Week 11
    3 Topics
    |
    1 Quiz
  12. The Cartesian Plane Co-ordinate System II | Week 12
    1 Topic
    |
    1 Quiz



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To factorize an expression, divide each term of the expression by their common factor. To factorize completely, use the Highest Common Factor (HCF). 

Example 8

Factorize completely 

(a) 2a + 4ab 

(b) 5x + 10y

(c) 15mn2 – 10m2n2

(d) \( \frac{2 \pi r}{T} \: + \: \frac{2 \pi r^2}{T^2} \: – \: \frac{2 \pi r^3}{T^3} \)

Solution 

(a) 2a + 4ab 

Step 1: find the HCF of 2a and 4ab 

Screen Shot 2021 05 05 at 3.39.58 PM

 HCF = 2 x a = 2a 

= 2a + 4ab

= 2a (1 + 2b) → last

(b) 5x + 10y 

Find the HCF of 5x and 10y  

Screen Shot 2021 05 05 at 4.15.43 PM

HCF = 5

5x + 10y = 5 (x + 2y) → last

(c) 15mn3 – 10m2n2

Find the HCF 

Screen Shot 2021 05 05 at 4.18.12 PM

HCF = 5 x m x n x n

= 5mn2

15mn3 – 10m2n2 = 5mn2 (3n – 2m) 

(d) \( \frac{2 \pi r}{T} \: + \: \frac{2 \pi r^2}{T^2} \: – \: \frac{2 \pi r^3}{T^3} \)

2\( \frac{2 \pi r}{T} \)+ \( \frac{2 \pi r^2}{T^2} \)– \( \frac{2 \pi r^3}{T^3} \)
π\( \frac{ \pi r}{T} \)+ \( \frac{ \pi r^2}{T^2} \)– \( \frac{\pi r^3}{T^3} \)
r\( \frac{r}{T} \)+ \( \frac{ r^2}{T^2} \)– \( \frac{r^3}{T^3} \)
\( \frac{1}{T} \)\( \frac{1}{T} \)+ \( \frac{ r}{T^2} \)– \( \frac{r^2}{T^3} \)
1+ \( \frac{ r}{T} \)– \( \frac{r^2}{T^2} \)

H.C.F = \( \scriptsize 2 \: \times \: \pi \: \times \: r \: \times \: \normalsize \frac{1}{T} \)

H.C.F = \(\frac{2 \pi r}{T} \)

\( \frac{2 \pi r}{T} \: + \: \frac{2 \pi r^2}{T^2} \: – \: \frac{2 \pi r^3}{T^3} \)

= \(\frac{2 \pi r}{T} \left (\scriptsize 1 \: + \: \normalsize \frac{r}{T} \: -\: \frac{r^2}{T^2} \right)\)

Evaluation 

Factorize completely each of the following 

  1. 4x2y  +  12xy2
  2. 17m  –  34m2
  3. 5k2  –  k 
  4. 35p  +  20p2
  5. 9ab  + 3a
  6. mn3  –  3gmn  –  g3m2n3
  7. \( \frac{mv}{t} \: -\: \frac{mu}{t} \)

Answer 

  1. 4xy (x + 3y)
  2. 17m (1 – 2m) 
  3. K (5k – 1) 
  4. 5p (7 + 4p) 
  5. 3a (3b + 1) 
  6. mn (n2 – 3g – g3mn2
  7. \( \frac{m}{t} \scriptsize (v \: -\: u) \)

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