Question

How do you simplify \[\left( 5{{x}^{2}}+3x+4 \right)+\left( 5{{x}^{2}}+5x-1 \right)\]?

Answer 1

Hint: In this problem, we have to simplify the given expression. We can first add the given two quadratic equations to combine it as we are given an additional sign between the two quadratic equations. We can then simplify the remaining terms by adding the similar terms with the variables and the constant to get a simplified form.

Complete step by step solution:
We know that the expression given to be solved is,
\[\left( 5{{x}^{2}}+3x+4 \right)+\left( 5{{x}^{2}}+5x-1 \right)\]
We can first add the given two quadratic equations to combine it as we are given an additional sign between the two quadratic equations.
We can remove the brackets as we have addition sign to add up the two equations, we get
\[\Rightarrow 5{{x}^{2}}+3x+4+5{{x}^{2}}+5x-5\]
Now we can rearrange the above step by adding the similar terms from the highest power to the constant,
\[\Rightarrow 5{{x}^{2}}+5{{x}^{2}}+5x+3x+4-5\]
Now we can simplify the above step, by adding the similar terms with the variables and the constant to get a simplified form.
\[\Rightarrow 10{{x}^{2}}+8x-1\]

Therefore, the simplified form of the given expression by adding the give two quadratic equation \[\left( 5{{x}^{2}}+3x+4 \right)+\left( 5{{x}^{2}}+5x-1 \right)\] is \[10{{x}^{2}}+8x-1\].

Note: Students make mistakes while adding the numbers of the respective coefficient. We can first add the terms which are the coefficient of \[{{x}^{2}}\], then we can add the coefficient of x terms then we can add the constant terms. In case if we have subtraction between two equations, we have to subtract the second equation from the first equation.