Question

Write the following in the product form: ${a^2}{b^5}$.

Answer 1

Hint: Polynomials are consisting of constants and variables. The values of constants are fixed
i.e. we know the value of constant e.g. 3, 7, 2 all are constant. The value of the variable is not fixed i.e. we don’t know the value. When some are not given to us then we can assume that value by taking a variable e.g. x, y, z all are variables.
If any number has power 3 then it means that number is multiplied by itself 3 times and we say it as cube e.g. ${3^3} = 3 \times 3 \times 3 = 27$.
If we have to find a cube of variable then it can be written in the product as follows:
${x^3} = x \times x \times x$

Complete step-by-step answer:
Given: - The polynomial is ${a^2}{b^5}$.
First of all, split them into constants and variables e.g. 4a. In 4a, 4 is the constant and a is variable.
The polynomial ${a^2}{b^5}$ consists of two variables ${a^2}$ and ${b^5}$.
Moreover, a has power 2, so we can write it as
$ \Rightarrow {a^2} = a \times a$
While b has power 5, so it can be written as,
$ \Rightarrow {b^5} = b \times b \times b \times b \times b$
So, ${a^2}{b^5}$ can be written as,
$\therefore {a^2}{b^5} = a \times a \times b \times b \times b \times b \times b$

Hence the product form of ${a^2}{b^5}$ is $a \times a \times b \times b \times b \times b \times b$.

Note: The three types of polynomial based on terms are discussed as follows:
Monomial: - If the number of terms in a polynomial is one then they are said to be Monomial.
E.g.$4x,2y,{x^3}$ etc.
Binomial: - If the number of terms in a polynomial is two then they are said to be Monomial. E.g. $6 +{y^2},x + z$ etc.
Trinomial: - If the number of terms in a polynomial is three then they are said to be Monomial.
E.g. $6{x^3}y + z + 4xz,5{x^7} + y + 14$ etc.