Question

How do you simplify $ - 2{y^3}(3{x^2}y - 6{x^2}{y^2})$?

Answer 1

Hint: In this question we will multiply the terms and expand the bracket to then use the property of exponents to simplify the expression. Finally we get the required answer.

Formula used: ${a^m}{a^n} = {a^{m + n}}$

Complete step-by-step solution:
We have the expression in the question as:
$ \Rightarrow - 2{y^3}(3{x^2}y - 6{x^2}{y^2})$
On multiplying the term $ - 2{y^3}$with the terms in the bracket, we get:
$ \Rightarrow ( - 2{y^3} \times 3{x^2}y) - ( - 2{y^3} \times 6{x^2}{y^2})$
Now on opening the brackets, we get:
$ \Rightarrow - 2{y^3} \times 3{x^2}y + 2{y^3} \times 6{x^2}{y^2}$
Now on multiplying the similar terms and the constants, we get:
$ \Rightarrow - 6{x^2}{y^3}y + 12{x^2}{y^2}{y^3}$
Now we know the property of exponents that ${a^m}{a^n} = {a^{m + n}}$, on applying this property on the above expression, we get:
$ \Rightarrow - 6{x^2}{y^{3 + 1}} + 12{x^2}{y^{2 + 3}}$
On simplifying the exponents, we get:
$ \Rightarrow - 6{x^2}{y^4} + 12{x^2}{y^5}$

$- 6{x^2}{y^4} + 12{x^2}{y^5}$ is the required answer.

Note: In this question we have used the property of exponents to simplify the expression.
It is to be remembered that exponents are used to write a term which is in multiplication multiple times in a simplified manner by giving powers to the term which indicates how much time the term is multiplied to itself.
The expression given to us in the question is a polynomial equation. A polynomial equation is an equation which is made up of coefficients and unknown variables.
The highest power of exponent in the polynomial is called the degree of the equation. The higher the degree is, the tougher it is to factorize the equation.
Because of the difficulty of exponential terms, logarithm is used which converts the exponential terms into multiplication terms.
It is to be remembered that when two negative terms are multiplied the product of both will be positive. This should be remembered while simplifying the parenthesis or the bracket in the expression.