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

Question:By using the factors of `x^2` - `y^2`, evaluate `96^2` - 36 

`x^2` - `y^2`
=(x+y)(x-y)
`:.` `96^2` - 36
= `96^2` - `6^2`
=(96+6) (96-6)
=102+90
=192

Question:3`y^2` + 81 

3`y^2` + 81
=3(`y^2`+27)

Question:Factorise `a^2` +2ab +`b^2` 

`a^2` +2ab +`b^2`
=`a^2` + ab +ab +`b^2`
=a(a+b) +b(a+b) 
=(a+b) (a+b)
=`(a+b)^2`

Question:What number must be added to (`x^2` +6x) to make the result a perfect square? 

(`x^2` + 6x)
=`x^2` + `2.x.3` + `3^2` - 9
=`(x+3)^2` - 9               [here `(x+3)^2` is perfect square ]

`:.`  to make (`x^2` +6x) perfect , 9 must be added

Question:what number must be added to (`x^2` -18x) to make the result a perfect square? 

(`x^2` -18x)
=`x^2` - 2 . x .9 +`9^2` - 81
=`(x-9)^2` - 81                        [ here `(x-9)^2` is perfect squire ]


`:.`  to make (`x^2` - 18x) perfect , 81 must be added

Question:Factorise  ax + 3a - xy -3y 

ax + 3a - xy -3y
=a(x+3) - y(x+3)
=(x+3) (a-y)