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6.2.2 Algebraic Expressions (III), PT3 Practice

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6.2.2 Algebraic Expressions (III), PT3 Practice
 
Question 6:
(a) Simplify each of the following:
(i) 12 m n 32 (ii) x 2 − x y x
(b) Express 1 2 q − 2 p − 7 6 q  as a single fraction in its simplest form.

Solution:
(a)(i) 12 m n 32 = 3 m n 8 (a)(ii) x 2 − x y x = x ( x − y ) x = x − y

(b)
1 2 q − 2 p − 7 6 q = 1 × 3 2 q × 3 − ( 2 p − 7 ) 6 q = 3 − 2 p + 7 6 q = 10 − 2 p 6 q = 2 ( 5 − p ) 3 6 q = 5 − p 3 q


Question 7:
  (a) Factorise 2ae + 3af – 6de – 9df
  (b)   Simplify a 2 − b 2 ( a + b ) 2

Solution:
(a)
2ae + 3af – 6de – 9df = a (2e + 3f ) – 3d (2e + 3f)
= (2e + 3f ) (a – 3d)

(b)
a 2 − b 2 ( a + b ) 2 = ( a + b ) ( a − b ) ( a + b ) ( a + b ) = a − b a + b


Question 8:
  (a) Factorise –8c2 – 12ac.
  (b)   Simplify a e + a d − 2 b e − 2 b d a 2 − 4 b 2 .  

Solution:
(a)
–8c2– 12ac
= –4c (2c + 3a)

(b)
a e + a d − 2 b e − 2 b d a 2 − 4 b 2 = a ( e + d ) − 2 b ( e + d ) ( a + 2 b ) ( a − 2 b ) = ( e + d ) ( a − 2 b ) ( a + 2 b ) ( a − 2 b ) = e + d a + 2 b


Question 9:
  (a) Factorise 12x2 – 27y2
  (b)   Simplify 3 m 2 − 10 m + 3 m 2 − 9 ÷ 3 m − 1 m + 3 .  

Solution:
(a)
12x2 – 27y2 = 3 (4x2 – 9y2)
= 3(2x – 3y) (2x + 3y)

(b)
3 m 2 − 10 m + 3 m 2 − 9 ÷ 3 m − 1 m + 3 = ( 3 m − 1 ) ( m − 3 ) ( m + 3 ) ( m − 3 ) × m + 3 3 m − 1 = 1
  

Question 10:
Simplify:  8m+mn 3m ÷ n 2 −64 24

Solution:
8m+mn 3m ÷ n 2 −64 24 = 8m+mn 3m × 24 n 2 −64 = m( 8+n ) 3m × 24 n 2 − 8 2 = m ( 8+n ) 3 m × 24 8 ( n−8 ) ( n+8 ) = 8 n−8