Question

(8m-3n)^2 - (4m+3n)^2​

Answer 1

`48m^2-72mn`

Explanation:

We need to solve
`(8m-3n)^2 - (4m+3n)^2`

We know that,

`(a+b)^2=a^2+b^2+2ab\\\\(a-b)^2=a^2+b^2-2ab`

Using the above formula,

`(8m-3n)^2 - (4m+3n)^2=(8m)^2+(3n)^2-2(8m)(3n)-[(4m)^2+(3n)^2+2(4m)(3n)]\\\\=64m^2+9n^2-48mn-(16m^2+9n^2+24mn)\\\\=64m^2+9n^2-48mn-16m^2-9n^2-24mn\\\\=48m^2-48mn-24mn\\\\=48m^2-72mn`

So, the final answer is
`48m^2-72mn`.