Question

How do you multiply \[4{p^4}qr.3{p^2}{q^5}{r^7}.10{p^5}{q^2}{r^3}\]

Answer 1

Hint: Here in this question, we have to find the product of 3 monomials. The monomial is one form of algebraic expression. So let we multiply 3 monomials which are different from one another and then we use the arithmetic operation that is multiplication and then we simplify.

Complete step-by-step solution:
The binomial concept will come under the topic of algebraic expressions. The algebraic expression is a combination of variables and constant. The alphabets are known as variables and the numerals are known as constants. In algebraic expression or equation, we have 3 types namely, monomial, binomial and polynomial.
Now let us consider the three monomial and they are \[4{p^4}qr\], \[3{p^2}{q^5}{r^7}\] and \[10{p^5}{q^2}{r^3}\]
Now we have to multiply the monomials, to multiply the monomials we use multiplication. The multiplication is one of the arithmetic operations.
Now we multiply the above 3 monomials we get
\[4{p^4}qr.3{p^2}{q^5}{r^7}.10{p^5}{q^2}{r^3}\]
Here dot represents the multiplication. First, we multiply the first two terms of the above equation. We group the constant, p terms, q terms and r terms separately we get
\[ \Rightarrow (4.3.10)({p^4}.{p^2}.{p^5})({q^5}.q.{q^2})(r.{r^7}.{r^3})\]
On multiplying we get
\[ \Rightarrow 120({p^4}.{p^2}.{p^5})({q^5}.q.{q^2})(r.{r^7}.{r^3})\]
As we know the property \[{a^m}.{a^n} = {a^{m + n}}\], so by applying the property we get
\[ \Rightarrow 120({p^{4 + 2 + 5}})({q^{5 + 1 + 2}})({r^{1 + 7 + 3}})\]
On simplification we have
\[ \Rightarrow 120{p^{11}}{q^8}{r^{11}}\]
Hence, we have multiplied the three monomials and obtained the monomial expression or equation. The product is also an algebraic expression.

Hence the correct answer is \[120{p^{11}}{q^8}{r^{11}}\].

Note: To multiply we use operation multiplication, multiplication of numbers is different from the multiplication of algebraic expression. In the algebraic expression it involves the both number that is constant and variables. Variables are also multiplied, if the variable is the same then the result will be in the form of exponent.