(3m-2n)^2 i dont know how to solve it

Question

I need to find the product

Answer 1

This is a binomial (two terms) and everyone needs to know the fast-track way to simplify it.

The rule is (A±B)² = A² ± 2AB + B²  where if the plus appears between A & B on the left, then the + appears in front of the middle term on the right; similarly, if the - appears between A & B, then the sign of the middle term is also negative.

 

Observe that the middle terms consists of all four parts appearing on the left, in this order: sign, 2, A, B; Squaring every binomial always produces a trinomial, with the middle term composed in this way. 

Answer 2

Hi Breanna,

 

(3m-2n)^2 means we need to square the expression inside the bracket. Squaring means we have to multiply the expression by itself. So,

(3m-2n)^2 = (3m - 2n)(3m - 2n) (distribute using FOIL)

= 9m^2 - 6mn - 6mn + 4n^2

= 9m^2 - 12mn + 4n^2