7.2 ANSWERS factorising

Answers

Exercise 1

Copy and fill in

a)  h( 8m + ... ) = 8hm + 9h

h( 8m + 9 ) = 8hm + 9h 

 

b)  a ( ... + ... ) = 2a² + a

a ( 2a + 1 ) = 2a² + a 

 

c)  k ( ... - ... ) = 5k² - 3k

k ( 5k - 3 )= 5k² - 3k

Exercise 2

Copy and factorise.

a)  4a + 6b   

2 ^. 2 ^. a        3 ^. 2 ^. b           

The common factor is 2. Put it outside the brackets!

= 2 ( 2a + 3b ) 

If you check  with multiplying out brackets you will get 4a + 6b again.

       

b)  4p - pq 

 4 ^. 1 ^. p          p ^. q ^. 1 

The common factor is 1p = p. Put it outside the brackets!

= p ( 4 - q ) 

If you check with multiplying out brackets you will get 4p - pq again.

 

c)  v² + 18v 

  v ^. v ^. 1       18 ^. 1 ^. v

The common factor is 1 ^. v = v. Put it outside the brackets!

= v ( v + 18 ) 

If you check with multiplying out brackets you will get v² + 18 again. 

 

d)  2w - 6 

2 ^. 1 ^. w       2 ^. 3

The common factor is 2. Put it outside the brackets!

= 2 ( w - 3 ) 

If you check with multiplying out brackets you will get 2w - 6 again.

 

e)  pr + pq

p ^. r            p ^. q 

The common factor is p. Put it outside the brackets!

= p ( r + q ) 

If you check with multiplying out brackets you will get pr + pq again.

  

f)  y² - 5y 

y ^. y           5 ^. y 

The common factor is y. Put it outside the brackets!

= y ( y - 5 )

If you check with multiplying out brackets you will get y²  - 5y again.

 

g)  3m² + 5m 

= m ( 3m + 5 ) 

 

h)  7kl - 20k

= k ( 7l - 20 )

 

i)  8uv - 3v 

= v ( 8u - 3 )

 

j)  3rt + 9r 

= 3r (t + 3 )

 

k) 12bc - 9c 

= 3c ( 4b - 3) 

 

l)  3z² + 6z 

= 3z ( z + 2 )

 

Exercise 3

Factorise, put as many factors as possible outside the brackets.

a)  3b² - 6a 

= 3 ( b² - 2a ) 

 

b)  3mn - 3m 

= 3m ( n - 1 ) 

 

c)  3mn - 9mc

= 3m (n - 3c )

 

d)  12xyz - 16xy

= 4xy ( 3z - 4 ) 

 

e)  2bv + 8by

= 2b ( v + 4y )

 

f)  5a²  - 15a³

= 5a² ( 1 - 3a ) 

Exercise 4

Factorise, put as many factors as possible outside the brackets.

a)  6v³ - 12v 

= 6v ( v² - 2 ) 

 

b)  25g² - 30g

=  5g ( 5g - 6 ) 

 

c)  10c²  + 5c²w

= 5c² ( 2 + w ) 

 

d)  6f ⁴ - 3f ² 

= 3f ² ( 2f ² - 1 ) 

 

e)  18q²bc + 12qb²c

= 6qbc ( 3q + 2b)

 

f)  p⁴ - p³ + p² 

= p² ( p² - p + 1 ) 

 

g)  4h²y + hy - hy²

= hy ( 4h + 1 - y )

 

h)  2j⁸ + 18j⁶ - 16j⁵

= 2j⁵ ( j ³ + 9j - 8 )

 

i)  9j³s²l - 6js²l²

= 3js²l ( 3j² - 2l )