Question

How do you subtract $7{x^2} + 4x - 9$ from $5{x^2} + 10x - 5$?

Answer 1

Hint: This equation is the quadratic equation. The general form of the quadratic equation is $a{x^2} + bx + c = 0$. Where ‘a’ is the coefficient of ${x^2}$, ‘b’ is the coefficient of x and ‘c’ is the constant term. In this question, we want to apply subtraction between two quadratic equations. For that, we will combine the like terms together and then subtract the coefficients of the like terms.

Complete step-by-step answer:
 In this question, two quadratic equations are $5{x^2} + 10x - 5$ and $7{x^2} + 4x - 9$.
Here, we want to subtract $7{x^2} + 4x - 9$ from $5{x^2} + 10x - 5$.
Therefore, we can write:
 $ \Rightarrow \left( {5{x^2} + 10x - 5} \right) - \left( {7{x^2} + 4x - 9} \right)$
First, let us open the brackets. The second bracket will be multiplied by 1. So, the sign of the terms will be changed in the second coefficient.
$ \Rightarrow 5{x^2} + 10x - 5 - 7{x^2} - 4x + 9$
Now, let us write the like terms together. The liked terms are those which have the same variable to the same power.
Therefore,
$ \Rightarrow 5{x^2} - 7{x^2} + 10x - 4x - 5 + 9$
Let us group the like terms into the bracket.
$ \Rightarrow \left( {5{x^2} - 7{x^2}} \right) + \left( {10x - 4x} \right) + \left( { - 5 + 9} \right)$
Now, simplify the brackets. Let us simplify the coefficients of the like terms. The subtraction of 5 and 7 is -2 of the liked term of ${x^2}$, the subtraction of 10 and 4 is 6 of the liked term of x, and the addition of -5 and 9 is 4 of the constant terms.
$ \Rightarrow - 2{x^2} + 6x + 4$
Hence, we subtract $7{x^2} + 4x - 9$ from $5{x^2} + 10x - 5$, the answer will be $ - 2{x^2} + 6x + 4$.

Note:
Before we solve this question, we should know the concept of like terms. The liked terms are those terms that have the same variable to the same power. That means the base is the same and also the coefficient of that base is also the same. Then group the like terms. Then apply the subtraction operation to solve the expression.