2.2.3 Factorisation and Algebraic Fractions, PT3 Practice


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

Solution:
(a)
12x– 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 ( n8 ) ( n+8 ) = 8 n8


Question 11:
(a)
Expand: x (2 + y)

(b)
Express  5 6y 3x5 12y  as a single  fraction in its simplest form.

Solution:
(a)
x (2 + y) = 2x + xy

(b)
5 6y 3x5 12y = 5×2 6y×2 3x5 12y = 10( 3x5 ) 12y = 103x+5 12y = 153x 12y = 3 ( 5x ) 12 4 y = 5x 4y


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