Factorise #(A^2- 1) (B^2- 1) + 4AB#?
2 Answers
Mar 1, 2018
Explanation:
When multiplying out 2 brackets, you use this technique.
In this case, this is called the difference of 2 squares, which always produces this
It will always give the square of one number minus the square of another.
It is the same for
=
Therefore, both can be factorised back into 2 brackets
and
So,
can be factorised to
Mar 1, 2018
Explanation:
#(A^2-1)(B^2-1)+4AB#
#= A^2B^2-A^2-B^2+1+4AB#
#= (A^2B^2+2AB+1)-(A^2-2AB+B^2)#
#= (AB+1)^2-(A-B)^2#
#= ((AB+1)-(A-B))((AB+1)+(A-B))#
#= (AB-A+B+1)(AB+A-B+1)#