Question

How do you simplify $2x + 3x - 5x\left( {2 + x} \right) + 4 - x\left( {3 + 4} \right)$?

Answer 1

Hint: In this question, we want to simplify the given expression into the standard form. For that, we apply the multiplication. We multiply each term of the first polynomial by each term of the second polynomial and then simplify. 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.

Complete step by step answer:
In this question, the given expression is:
$ \Rightarrow 2x + 3x - 5x\left( {2 + x} \right) + 4 - x\left( {3 + 4} \right)$
First, let us add 3 and 4 to remove the bracket.
$ \Rightarrow 2x + 3x - 5x\left( {2 + x} \right) + 4 - x\left( 7 \right)$
That is equal to,
$ \Rightarrow 2x + 3x - 5x\left( {2 + x} \right) + 4 - 7x$
Now, let us remove the brackets. For that, multiply the polynomial $ - 5x$ with $2 + x$. The answer is $ - 10x - 5{x^2}$.
Therefore,
$ \Rightarrow 2x + 3x - 10x - 5{x^2} + 4 - 7x$
Now, let us combine the like terms together. The liked terms are defined as the terms that contain the same variable which is raised to the same power, only the numerical coefficients can vary.
Therefore,
$ \Rightarrow - 5{x^2} + 2x + 3x - 10x - 7x + 4$
Now, let us simplify the like terms.
$ \Rightarrow - 5{x^2} - 12x + 4$

Hence, the answer of the given expression is $ - 5{x^2} - 12x + 4$.

Note: 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. Here, ‘a’, ‘b’, and ‘c’ are known values, ‘x’ is the variable or unknown. And ‘a’ can’t be 0. The solution of the quadratic equation is where it is equal to zero. They are also called roots or zeros.
Here is a list of methods to solve quadratic equations:
1. Factorization
2. Completing the square
3. Using graph
4. Quadratic formula