Question

Find the product of the monomial -4p, 7pq

Answer 1

Hint: We start solving this problem by first checking if there are any variables common in the given monomials and then multiply them using the formula, ${{a}^{m}}\times {{a}^{n}}={{a}^{m+n}}$. Then we multiply the numbers present in the monomials along with the signs by using the property, multiplication of plus and minus gives minus. Then we write the result by combining the obtained results and remaining variables in the monomials.

Complete step by step answer:
Here we need to find the value of $-4p\times 7pq$.
While multiplying the monomials, we need to check if they have any variables common. If there are any common variables then we will multiply them.
As the monomials are -4p and 7pq we can see that both of them have p common in them.
So, now let us multiply both the p’s present in them, that is $p\times p$.
Now let us consider the formula,
${{a}^{m}}\times {{a}^{n}}={{a}^{m+n}}$
Using it we get,
$\begin{align}
  & \Rightarrow p\times p={{p}^{1+1}} \\
 & \Rightarrow p\times p={{p}^{2}}........\left( 1 \right) \\
\end{align}$
Now let us consider the numbers that are in the monomials, that are -4 in the first monomial and 7 in the second monomial.
Let us now multiply them, that is we need to find the value of $-4\times 7$.
We can see that there is a minus sign in the above multiplication.
Now let us consider the property of multiplication of signs minus and plus.
When a minus is multiplied with a minus, we get plus.
When a plus is multiplied with plus, we get plus.
When a minus is multiplied with plus, we get minus.
So, using this property, as there is a product of a minus and a plus in $-4\times 7$, we get the sign minus.
So, we get the value of $-4\times 7$ as,
$\Rightarrow -4\times 7=-28.........\left( 2 \right)$
Now from equations (1) and (2) we get,
$\Rightarrow -4p\times 7pq=-28{{p}^{2}}q$
Hence answer is $-28{{p}^{2}}q$.

Note: The common mistake one makes while solving this problem is one might not consider the properties of multiplication of signs and just multiply the monomials 4p and 7pq and write the answer as $28{{p}^{2}}q$.