Question

Find the product of $2x\left( {3x + 5xy} \right)$.

Answer 1

Hint: This type of question is based on algebraic expression and operations done in them. This question consists of integers and variables so by using multiplication operations we will find the product of them. Some rules that are to be remembered while multiplying algebraic expressions are that product of two factors having the same sign whether it is positive or negative gives a positive outcome and product of two factors having unlike sign gives a negative outcome. We will add the power of the term having the same base and multiply the integer to get the desired answer.

Complete step by step solution:
We have to find the product of Algebraic expression:
$2x\left( {3x + 5xy} \right)$
The above expression consists of two different variables and two factors so it will be solved as follows:
We will multiply the two brackets as below:
$\begin{align}
& \Rightarrow 2x \left( {3x + 5xy} \right) \\
& \Rightarrow 2 \times 3 \times {x^1} \times {x^1} + 2 \times 5 \times {x^1} \times {x^1} \times y \\
\end{align}$
Now, we will add the power of the variable and get,
$\begin{align}
   & \Rightarrow 6{x^{1 + 1}} + 10{x^{1 + 1}}y \\
   & \Rightarrow 6{x^2} + 10{x^2}y \\
\end{align} $
We got the answer after simplifying as $6{x^2} + 10{x^2}y$.
Hence product of $2x\left( {3x + 5xy} \right)$ is $6{x^2} + 10{x^2}y$.

Note: The algebraic expression having more than one term which are made up of variables, coefficient and constant is known as Polynomial expression and they can be combined by using various mathematical operations such as subtraction, addition, multiplication and division. If the expressions have fraction power or negative exponent of a variable it is no longer a polynomial expression. The polynomial expression having two terms or variables is known as Binomial expression. If a variable is multiplied such that its power is ${x^a}$ and ${x^b}$ the outcome is ${x^{a + b}}$.