16y^2-x^2-6x-9. How can I factorise this? I know that -(x^2+6x+9) is equal to -(X+3)^2, and 16y^2 can be written as (4y)^2 but I can't quite get the solution (4y-x-3)(4y+X+3)

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Answer 1 · 2018-02-28T08:37:12

#16y^2-x^2-6x-9=(4y-x-3)(4y+x+3)#

First observe that #16y^2-x^2-6x-9#

= #16y^2-(x^2+6x+9)#

= #(4y)^2-(x+3)^2#

Now observe that this is of type #A^2-B^2#, where #A=4y# and #B=(x+3)#. Now factors of #A^2-B^2=(A-B)(A+B)#

Hence we can write #(4y)^2-(x+3)^2# as

#(4y-(x+3))(4y+(x+3))#

= #(4y-x-3)(4y+x+3)#