Question

How do you find the product of \[-2{{x}^{2}}({{x}^{2}}-3)\] ?

Answer 1

Hint: In the given question we can see we have a total of three terms. Our first step is to distribute each term of the first polynomial to every term of the second polynomial. Since, here we have only one term in the first polynomial thus distributing it to the rest of the two terms of the second polynomial. After that it is simple, we just have to multiply the coefficients with coefficients and variables with variables

Complete step-by-step answer:
This question belongs to the concept of simple multiplication of monomials by polynomials subtopic of algebra.
Before solving the question let us know what is polynomial and monomial.
So, polynomials are expressions which have constants, variables, exponents and are combined using mathematical operations such as subtraction, addition, multiplication, division and many more. Depending upon the number of terms polynomials are divided into monomials, binomials, trinomial, quadrinomial.
Here we have two polynomials for multiplication, one is monomial (having one term) and the other is binomial (having two terms). Let’s see how to multiply both the polynomials.
Here we have \[-2{{x}^{2}}({{x}^{2}}-3)\]. So, first we have to distribute the terms, after distributing we get.
\[-2{{x}^{2}}\times {{x}^{2}}-(-2{{x}^{2}}\times 3)\]
Now, simply multiply
\[\Rightarrow ~~~-2{{x}^{4}}+6{{x}^{2}}\]
Hence, the result of multiplication is \[-2{{x}^{4}}+6{{x}^{2}}\]

Note: Remember that when you are going to multiply the two terms with each other you must have to multiply the coefficients and add the exponents or powers of the variable. Also, in this case the calculations are not complex but with increasing degree of variables problems become complex thus there is a chance of silly mistakes. Do not forget to multiply the signs correctly.