Question

How do you subtract \[( - 16{x^2} - 19x - 10)\] and \[( - 18{x^2} - 13x - 14)\]?

Answer 1

Hint: We have an addition and subtraction of an algebraic expression. An algebraic expression is a combination of constants, variables and operators. The addition and subtraction of algebraic expressions are quite similar to the addition and subtraction of the number, when it comes to algebraic expression we must sort the like terms and unlike terms together.

Complete step by step answer:
Given,
We need to subtract \[( - 16{x^2} - 19x - 10)\] and \[( - 18{x^2} - 13x - 14)\].
That is
 \[ \Rightarrow ( - 16{x^2} - 19x - 10) - ( - 18{x^2} - 13x - 14)\]
Now we need to multiply second parentheses term by negative 1 then we have,
 \[ \Rightarrow - 16{x^2} - 19x - 10 + 18{x^2} + 13x + 14\]
Now grouping \[{x^2}\], x and constant terms we have,
\[ \Rightarrow - 16{x^2} + 18{x^2} - 19x + 13x - 10 + 14\]
Now adding we have,
\[ \Rightarrow 2{x^2} - 5x + 4\]
This is the required answer.

Note: Here we have a subtraction of two quadratic polynomials. You must be aware of the like and the unlike terms when you are adding or subtracting algebraic expressions. We can only perform the addition or subtraction on the like terms only. Like terms are the ones who have the same variables and exponents and the unlike terms are the one that have different variables. Here \[ \Rightarrow 2{x^2} - 5x + 4\], \[{x^2}\] and ‘x’ have the same variable but different exponent, hence they are unlike terms and we cannot simplify further. We solve the obtained result by factorization method or by quadratic formula method.