Consider the binomial A^2-B^2, and use the fact that the greatest common factor (GCF) between A^2 and B^2 is 5mk to write expressions for A and B.
Example binomial: (5mk)^2-(sqrt(5mk))^2 = 25m^2k^2 - 5mk Factored form: 5mk(5mk-1)
Practice makes perfect
We are interested in writing a binomial that is the difference of two perfect squares. The final binomial must have the following form.
A^2 - B^2
We are told that the greatest common factor (GCF) of our binomial must be 5mk. In consequence, we can write the equations below.
A^2 = 5mk * P_1 & (I) B^2 = 5mk* P_2 & (II)
In the expression above P_1 and P_2 have no factors in common. For simplicity we can consider P_1 = 5mk, and that way we get a perfect square with an integer base.
A^2 = 5mk* 5mk = (5mk)^2
⇓
A = 5mk
Next, we can consider P_2=1.
B^2 = 5mk* 1 = 5mk
⇓
B = sqrt(5mk)
Finally, let's substitute A=5mk and B=sqrt(5mk) into our initial binomial and factor it.
