Simplify the following expression: $4y\left( 3{{y}^{2}}+5y-7 \right)+2\left( {{y}^{3}}-4{{y}^{2}}+7 \right)$

Hint: We will first multiply the given expression as shown by opening the brackets and then we will rearrange some terms in descending order of power of y and that will be the final answer for this question.

Complete step-by-step solution -
Now let’s try by multiplying the given expression by opening the brackets,
$\begin{align}
  & 4y\left( 3{{y}^{2}}+5y-7 \right)+2\left( {{y}^{3}}-4{{y}^{2}}+7 \right) \\
 & =4y\times 3{{y}^{2}}+4y\times 5y-7\times 4y+2\times {{y}^{3}}-2\times 4{{y}^{2}}+2\times 7 \\
\end{align}$
As we have opened the bracket now we will multiply it,
$=12{{y}^{3}}+20{{y}^{2}}-28y+2{{y}^{3}}-8{{y}^{2}}+14$
Now we will club together the same powers of y and then we will perform the given addition or subtraction as per given in the question,
$\begin{align}
  & =(12{{y}^{3}}+2{{y}^{3}})+(20{{y}^{2}}-8{{y}^{2}})-28y+14 \\
 & =14{{y}^{3}}+12{{y}^{2}}-28y+14 \\
\end{align}$
Hence, after doing the subtraction and addition we get our final answer as :
$=14{{y}^{3}}+12{{y}^{2}}-28y+14$
Hence, we have solved the equation and converted it into a simpler form.

Note: There might be some students who can make some calculation mistakes while solving the question so it’s always better to quickly check by putting some values in place of y and then we can check whether the two forms of the equation will give same answer or not, if the answer are same then there is no mistake but if the answer comes out to be different then there might be some calculation mistake and with that we can avoid any error.