Question

How do you write \[\left( -3x-1 \right)\left( x+1 \right)\] in standard form?

Answer 1

Hint: In the question that has been mentioned above we have been given an equation which has only one variable but will result in quadratic form. The form cannot be stated as a standard form as two different brackets are in multiplication to each other and the values which are in the bracket are linear equations so we need to remove those two brackets and write the whole equation as a standard form of a quadratic equation.

Complete step by step answer:
In the above mentioned question we need to write the standard form of a linear equation which is:
\[a{{x}^{2}}+bx+c\]
We need to write the given equation in the same format as mentioned above for this we are going to first open the brackets by taking one of the linear equations out of the two and use the values to multiply it with the other, basically let us say that we are going to take the first bracket’s linear equation i.e.(-3x-1) from this linear equation we are first going to take -3x and then multiply it with the values of the next linear equation one by one i.e. first by x and then multiply it by 1 then again do the same thing with -1 which is the second term of the first linear equation by doing this we will be able to open the brackets and will see a new equation which will be close to a quadratic equation. After opening the bracket we will get:
\[=-3{{x}^{2}}-3x-x-1\]
Now after we have opened the brackets we can there are two different values of x so we will add both the values of x and we will get the final equation i.e. the required standard equation which we will get as:
\[=-3{{x}^{2}}-4x-1\]
So the standard form of the equation given in the question is \[=-3{{x}^{2}}-4x-1\].

Note:
For solving this type of question we need to first know what type of equation is it, in this question we can see that both the brackets have one x value on it so this equation will turn out to be a quadratic function if it had been \[{{x}^{2}}\] and x the it would have become a polynomial function so when we have figured out what type of function will be forming we will easily be able to convert the given equation in into its standard form by comparing the standard equation and the equation given in the question.