What is the error and how do I explain it

Question

asked Dec 4, 2023 157k views

1 Answer

Yashwanth Kata · Answer 1 · 2023-12-10T00:48:59+0000

Recalll that the image is analyzing the expression

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

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