Question

Using the identity $(x+a)(x+b)=x^2+(a+b)x+ab$, find out the following products:
$(2m+3n)(2m+4n)$

Answer 1

using $(x+a)(x+b)=x^2+ba+(a+b)x$

For the above expression, keeping $a=3n$ and $b=4n$, we get

$(2m+3n)(2m+4n)=(2x{)}^2+(3n+4n)2m+3n\times 4n=4x^2+14mn+12n^2$