Question

How do you subtract $3{{x}^{2}}-4$ from the sum of ${{x}^{2}}-6x+1$ and $2{{x}^{2}}-5x+5$ ?

Answer 1

Hint: In this question, we have to solve the equations to get a unique equation using mathematical operators. Therefore, we will use the basic mathematical rules and the BODMAS method to solve the equations. We will first rewrite the statement into the mathematical statement and then solve it further. Since the problem gives three equations, we will first solve the last two equations because they are adding to each other and then we will subtract the new equation to the first equation. Then we will apply the BODMAS method in the equation and make the necessary calculations, to get the required result for the problem.

Complete step by step answer:
According to the question, we have to solve the statement.
So, we will use the basic mathematical rules and the BODMAS method to solve the same.
 The statement given to us is subtract $3{{x}^{2}}-4$ from the sum of ${{x}^{2}}-6x+1$ and $2{{x}^{2}}-5x+5$ .
Therefore, we will first rewrite the given statement into the mathematical statement, that is $\left( ({{x}^{2}}-6x+1)+(2{{x}^{2}}-5x+5) \right)-\left( 3{{x}^{2}}-4 \right)$ ---------- (1)
Now, we will apply the BODMAS method in the equation (1), that is we will first open the brackets of the brackets, we get
$\left( {{x}^{2}}-6x+1+2{{x}^{2}}-5x+5 \right)-\left( 3{{x}^{2}}-4 \right)$
Now, we will solve the bracket of the above equation, we get
$\left( 3{{x}^{2}}-11x+6 \right)-\left( 3{{x}^{2}}-4 \right)$
Now, we will again open the brackets, therefore, we get
$3{{x}^{2}}-11x+6-3{{x}^{2}}+4$
Thus, we see that after opening the second bracket -4 will become 4 because $-(-4)=4$ , therefore on further solving, we get
$-11x+10$ which is our required answer.
Therefore, for the statement subtract $3{{x}^{2}}-4$ from the sum of ${{x}^{2}}-6x+1$ and $2{{x}^{2}}-5x+5$ , its simplified value is $-11x+10$ .

Note:
While solving this problem, keep in mind that when we rewrite the question statement into the mathematical statement the first term is subtracting from the sum of the other two, which implies that if we are subtracting b from a, this means that $a-b$ instead of $b-a$ . Also, make all the calculations properly to avoid mathematical errors and write each step properly to avoid confusion.