Question

III) Find the binomial factors8n2 2mn – 3m2 + 12mn

Answer 1

The given expression is

$8n^2-2mn-3m^2+12mn$

Let's group the terms in order to factor out the greatest common factor of each

$(8n^2-2mn)+(-3m^2+12mn)$

Notice that the greatest common factor in the first binomial is 2n, and the greatest common factor of the second binomial is 3m. Let's factor them out

$2n(4n-m)+3m(-m+4n)=2n(4n-m)+3m(4n-m)$

As you can observe, 4n-m is a common factor, so we have to factor it out too

$(4n-m)(2n+3m)$

Hence, the binomial factors are

$(4n-m)(2n+3m)$