Question

What is the value of expression \[2{{x}^{5}}y.3{{x}^{2}}y\]?

Answer 1

Hint: An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, multiplication, division). Expressions are made up of terms. They are also termed algebraic equations.

Complete step by step solution:
In mathematics, an algebraic expression is an expression built up with integer constants, variables, and algebraic operations (i.e addition, subtraction, multiplication, division) and exponentiation by an exponent that is a rational number.
So, reading the question carefully, we came to know that \[2{{x}^{5}}y.3{{x}^{2}}y\] is the given expression.
By clear observation of the given mathematical expression, we can see constants (i.e \[3\],\[2\]),
We can see variables \[x,y\] with exponential powers as \[5,2\] and \[1,1\] respectively.
So now, it is clear that \[2{{x}^{5}}y.3{{x}^{2}}y\] is an ALGEBRAIC EXPRESSION because It consists of all the terms what algebraic expression consists.
So now we can conclude that \[2{{x}^{5}}y.3{{x}^{2}}y\] is an algebraic expression
 Further we can simplify the given equation.
From the basic algebraic formula, we know that \[{{x}^{a}}\times {{x}^{b}}={{x}^{a+b}}\]
This basic formula can be applied here. To apply this first we should bring all similar terms together.
So, we can modify given equation as \[2\times 3\times {{x}^{5}}{{x}^{2}}\times {{y}^{1}}{{y}^{1}}\]
Now multiplying \[2\] and \[3\] we get \[6\]
So, the equation becomes
\[\Rightarrow \]\[6\times {{x}^{5}}{{x}^{2}}\times {{y}^{1}}{{y}^{1}}\]
Now applying the formula \[{{x}^{a}}\times {{x}^{b}}={{x}^{a+b}}\] we get the new equation as,
\[\Rightarrow \]\[6\times {{x}^{5+2}}\times {{y}^{1+1}}\]
After simplification we get simple equation as
\[\Rightarrow \]\[6\times {{x}^{7}}\times {{y}^{2}}\]
By observing the equation clearly, we can see that the equation consists of only one constant (i.e \[6\]) and only two variables (i.e \[x,y\]).
Now we can conclude that the given equation \[2{{x}^{5}}y.3{{x}^{2}}y\] is an ALGEBRAIC EXPRESSION.

Note: Students should know the clear concept because WRONG CONCEPT can lead to doing this type of questions wrong. Also, students should know exactly what are constants and variables from the given question.