Question

What is the error and how do I explain it

Answer 1

Recalll that the image is analyzing the expression

`(k+4)^2`

To identify the mistake, we will operate this expression and see we can get. By the properties of exponentiation, we have that

`(k+4)^2=(k+4)\cdot(k+4)`

Now, we will use the distributive property of multiplication on the right side, so we get

`(k+4)\cdot(k+4)=k\cdot(k+4)+4\cdot(k+4)`

Let us apply the distributive property once more to each part, so we have that

`k\cdot(k+4)=k\cdot k+4\cdot k=k^2+4k`

and

`4\cdot(k+4)=4\cdot k+4\cdot4=4\cdot k+4^2`

So, if we add this two results, we have

`(k+4)^2=k^2+4k+4k+4^2=k^2+8k+4^2`

Notice that the mistake is that the image is omitting the expression in the middle (4k+4k)