Question

Find each of the following products:-
\[6a\times 4{{b}^{2}}\]
b) \[7m\times 5{{n}^{2}}\times 4n\]

Answer 1

Hint:For solving such questions, we have to multiply the constants first and then we have to multiply the variables, and then we will multiply the constant with the variable.

Complete step by step answer:
Let us take an example: \[4y\times 8w\times 3{{y}^{2}}\]
We will firstly multiply the constants:-
\[4\text{ }\times \text{ }8\text{ }\times \text{ }3\text{ }=\text{ }12\text{ }\times \text{ }8\text{ }=\text{ }96\]
Now, we will multiply the variables:-
\[y\text{ }\times \text{ }w\text{ }\times \text{ }{{y}^{2}}=\text{ }{{y}^{3}}\times \text{ }w\text{ }=\text{ }w{{y}^{3}}\]
Let us now multiply the constant and variable:-
\[96\text{ }\times \text{ }w{{y}^{3}}=\text{ }96w{{y}^{2}}\]
Let us now solve the question:-

\[6a\times 4{{b}^{2}}\]
We will firstly multiply the constants:-
\[6\text{ }\times \text{ }4\text{ }=\text{ }24\]
Now, we will multiply the variables:-
\[a\text{ }\times \text{ }{{b}^{2}}=\text{ }a{{b}^{2}}\]
Let us now multiply the constant and variable:-
\[24\text{ }\times \text{ }a{{b}^{2}}=\text{ }24a{{b}^{2}}\]
The product of 6a and 4b2 is 24ab2

\[7m\text{ }\times \text{ }5{{n}^{2}}\times \text{ }4n\]
We will firstly multiply the constants:-
\[7\times 5\times 4\text{ }=\text{ }7\times 20\text{ }=\text{ }140\]
Now, we will multiply the variables:-
\[m\text{ }\times \text{ }{{n}^{2}}\times \text{ }n\text{ }=\text{ }m\text{ }\times \text{ }{{n}^{3}}=\text{ }m{{n}^{3}}\]
Let us now multiply the constant and variable:-
\[140\text{ }\times \text{ }m{{n}^{3}}=\text{ }140m{{n}^{3}}\]
The product of 7m, 5n2 and 4n is 140mn3

Note:One must do all the calculations very carefully for solving this question.Also, not only in this question, one must be very careful while doing such questions as any mistake in the calculus can make the answer wrong.