Question

(n square-8n+16)÷(n-4)​

Answer 1

Given:

$\frac{n^{2} -8n+16}{n-4}$

To Do:

We just have to simplify the given expression.

Solution:

We can see that we have a bigger numerator and a smaller denominator, so the first thing that should come up in our mind is to make the numerator simplified by some methods first then if we would have anything common between numerator and denominator it would surely help us in making the expression short and simplified. We can see that the numerator is a quadratic expression so can we do here factorization? Of course!. Now, how we are going to do that? There is a method called splitting the middle term. What we have to do is we need  to rewrite the middle term of the quadratic expression as the sum or difference of the two terms in such a way that the product of coefficient of those terms equals the last term of the quadratic expression.

Let us consider a quadratic equation(Numerator):

$n^{2} -8n+16$

Middle term's coefficient:

$-8$

Last Term:

$16$

We could observe that if we rewrite -8 as -4-4 then -4x-4 would give us 16 which is the last term and its sum is giving the coefficient of the middle term.

We're good to go as follows:

1. $n^{2}-4n-4n+16$

2.$n(n-4)-4(n-4)$ (Take the commons)

3.$(n-4)(n-4)$

Simplified Numerator is: $(n-4)(n-4)$

The expression becomes:$\frac{(n-4)(n-4)}{(n-4)}$

After cutting the common terms in numerator and denominator, the final answer becomes: $(n-4)$

So the answer is (n-4).