Question

How do you find $h\left( { - 2n} \right)$ given $h\left( n \right) = {n^2} + n$?

Answer 1

In this question we have to find the value of the expression when$n = - 2n$ ,so we input the given value inside the given polynomial, thus substitute the value in place of $n$in the polynomial given in the question and further simplification using the operations addition, subtraction we will get the required value.

Complete step by step solution:
An algebraic expression is a mathematical term that consists of variables and constants along with mathematical operators (subtraction, addition, multiplication, etc.).
Given polynomial is $h\left( n \right) = {n^2} + n$,
As the degree of the polynomial is 2 so, the polynomial is a quadratic polynomial.
We have to find the value of the given expression when $n = - 2n$, so substitute the value in place of$n$in the given polynomial $h\left( n \right) = {n^2} + n$, we get,
$\Rightarrow h\left( { - 2n} \right) = {\left( { - 2n} \right)^2} + \left( { - 2n} \right)$,
Now simplifying the right hand side by taking the square in the polynomial, we get,
$\Rightarrow h\left( { - 2n} \right) = 4n + \left( { - 2n} \right)$,
Now further simplification in the right hand side by taking out the brackets, we get,
$\Rightarrow h\left( { - 2n} \right) = 4n - 2n$,
Now subtracting for further simplification, we get,
$\Rightarrow h\left( { - 2n} \right) = 2n$,
So, the value of the polynomial when$n = - 2n$ is $2n$.
Final Answer:
$\therefore$ The value of the expression $h\left( n \right) = {n^2} + n$ when $n = - 2n$ will be equal to $2n$.

Note:
To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.