6.2.1 Algebraic Expressions (III), PT3 Practice


6.2.1 Algebraic Expressions (III), PT3 Practice

Question 1:
(a)(i) Factorise 18a + 3
(a)(ii) Expand –3 (–y + 5)
(b) Express 56y3x512y as a single fraction in its simplest form.

Solution:
(a)(i) 18+ 3 = 3(6a + 1)
 
(a)(ii) –3 (–+ 5) = 3y – 15
 
(b)
56y3x512y=5×26y×2(3x5)12y=103x+512y=153x12y=3(5x)412y=5x4y


Question 2:
(a) Expand:
 (i) 3 (–a + c)
 (ii) –5 (c)
(b) Factorise 4+ 2
(c) Simplify: 3x+6x24÷x+2x2   

Solution:
(a)(i) 3 (–+ c) = –3a + 3c
 
(a)(ii) –5 (c) = –5a + 5c
 
(c)
3x+6x24÷x+2x2=3(x+2)(x+2)(x2)×x2x+2=3x+2



Question 3:
(a) Factorise:
 (i) 5m + 25
 (ii) 7x + 9xy
(b) Simplify: 4x124y÷x29yz

Solution:
(a)(i)5m + 25 = 5 (m + 5)
 
(a)(ii)7x + 9xy = x (7 + 9y)

(b)4x124y÷x29yz=4(x3)4y×yz(x+3)(x3)=zx+3


Question 4:
  (a) Factorise completely:
  4 – 100n2
(b) Express 45x710y15x  as a single fraction in its simplest form.

Solution:
(a)
4 – 100n2= (2 + 10n)(2 – 10n)
(b)
45x710y15x=4×35x×3(710y)15x=127+10y15x=5+10y15x=5(1+2y)315x=1+2y3x


Question 5:
  (a) Simplify:
(m – 4n)(m + 4n) – m2
  (b) Simplify: 3x3yx+y×2x+2y6x  

Solution:
(a)
(m – 4n)(+ 4n) – m2
= m2 + 4mn – 4mn – 4n2m2
= 0
 
(b)
3x3yx+y×2x+2y6x=3(xy)x+y×2(x+y)6x=xyx