Question

How do you simplify the expression $\left( 5{{x}^{2}}+10x-5 \right)-\left( 4{{x}^{2}}-6x+1 \right)$?

Answer 1

Hint: We have to find the like terms in $\left( 5{{x}^{2}}+10x-5 \right)-\left( 4{{x}^{2}}-6x+1 \right)$ and then simplify them. We check the algebraic terms in the equation of $\left( 5{{x}^{2}}+10x-5 \right)-\left( 4{{x}^{2}}-6x+1 \right)$ and also the power values. Terms with the same degree and same algebraic forms will be combining the like terms.

Complete step-by-step solution:
In the equation of $\left( 5{{x}^{2}}+10x-5 \right)-\left( 4{{x}^{2}}-6x+1 \right)$, the only variable term is $x$.
We apply the binary operation of subtraction to get
$\begin{align}
  & \left( 5{{x}^{2}}+10x-5 \right)-\left( 4{{x}^{2}}-6x+1 \right) \\
 & =5{{x}^{2}}+10x-5-4{{x}^{2}}+6x-1 \\
\end{align}$
There are three types of power or indices values for variable $x$.
The terms $5{{x}^{2}}$ and $-4{{x}^{2}}$ are like terms as they have the same variable and the indices value is also the same which is 2.
Similarly, the terms $10x$ and $6x$ are like terms as they have the same variable and the indices value is also the same which is 1.
We now simplify the like terms using the binary operation between them.
We add $5{{x}^{2}}$ and $-4{{x}^{2}}$ to get \[5{{x}^{2}}-4{{x}^{2}}={{x}^{2}}\].
Then we add $10x$ and $6x$ to get $10x+6x=16x$.
At the end we add the constants and get $-5-1=-6$
The combined solution will be
$\begin{align}
  & 5{{x}^{2}}+10x-5-4{{x}^{2}}+6x-1 \\
 & ={{x}^{2}}+16x-6 \\
\end{align}$
This way we simplify $\left( 5{{x}^{2}}+10x-5 \right)-\left( 4{{x}^{2}}-6x+1 \right)$ and get ${{x}^{2}}+16x-6$.

Note: In the calculation we must be careful about the number of variables available in the terms. Unlike terms can be created with different variables but same indices value. In compound terms we check the individual indices.