Question:Evaluate 7`xx`19.3+8`xx`19.3-5`xx`19.3 

7`xx`19.3+8 `xx` 19.3 - 5`xx`19.3
 =19.3(7+8-5)
 =19.3 `xx`10
 =193

Question:Evaluate 19.3`pi` - 15.8`pi` 

19.3`pi` - 15.8`pi` =`pi`(19.3-15.8)=`pi` `xx`3.5 

                                   = `22/7 xx 7/2`

                                   = 11

Question:Factories ax+bx+ay+by 

ax+bx+ay+by = (ax+bx) + (ay+by)
                       = x(a+b) +y (a+b)
                       =(a+b) (x+y).

Question:Factorise  ax + ay -x -y . 

ax + ay -x -y=a(x+y) - (x+y) 
                    =(x+y) (a-1).

 Notice that when the last two terms are grouped with a minus sign outside. the signs of both terms in the bracket must be changed.

                    ax + ay -x -y=a(x+y) - (x+y) 
 and not     
                   a(x+y) - (x-y) .

It is good plan to remove the brackets mentally to check your working.

Question:Factorise `xx^2`y - `xxy^2`+3y -3`xx` 

`xx^2`y - `xxy^2`+(3y -3`xx`) = xy(x-y) +3(y-x)

This has no obvious factor as the expression inside the brackets are different .
  but if we arrange the expression as 
   
`xx^2`y - `xxy^2`-3`xx`+3y) = `xx`y(x-y) -3(x-y),

An obvious factor is now apparent.
The factors are (x-y)(xy-3).

Question:Factorise `xx^2`+9x+20. 

`xx^2`+9x+20

=`xx^2`+5x +4x +20

=x(x+5)+(x+4)

=(x+5)  (x+4)

Question:`xx^2` -2x -15 

`xx^2` -2x -15
=`xx^2` -5x + 3x -15
=x(x-5)+3(x-5)
=(x-5) (x+3)

Question:6`xx^2` + 11xy - 10`y^2` 

6`xx^2` + 11xy - 10`y^2`
=6`xx^2`+ 15xy - 4xy - 10`y^2`
=3x(2x +5y) -2(2x+5y)
=(3x-2y) (2x+5y)

Question:Factorise `y^2`- y - 42 

`y^2`- y - 42 
=`y^2`- 7y + 6y - 42
=y(y+7) + 6(y-7)
=(y-7) (y+6)

Question:Factorise `x^2` - `y^2` and hence evaluate `100^2` - `99^2` 

`x^2` - `y^2`
=(x+y) (x-y)
`:.` `100^2` - `99^2`
=(100+99) (100-99)
=199+1
=200