Question

identify how many terms will be in the expanded form of a polynomial equivalent to the following expression. (−6m–n)2

Answer 1

There are three terms in the expanded form of the given polynomial expression
`(-6m-n)^2` equivalent to the expression
`36m^2+12mn+n^2`

Therefore
`(-6m-n)^2=36m^2+12mn+n^2`

Explanation:

Given expression is
`(-6m-n)^2`

To simplify the given expression as below:

`(-6m-n)^2`

`=((-6m)+(-n))^2`

(Using the property
`(a+b)^2=a^2+2ab+b^2`)

Here a=-6m and b=-n

`=(-6m)^2+2(-6m)(-n)+(-n)^2`

`=6^2.m^2+12mn+n^2`

`=36m^2+12mn+n^2`

`(-6m-n)^2=36m^2+12mn+n^2`

Therefore
`(-6m-n)^2=36m^2+12mn+n^2`

There are three terms in the expanded form of the given polynomial expression
`(-6m-n)^2` equivalent to the expression
`36m^2+12mn+n^2`