Question

Evaluate: -$10y\left( 6y+21 \right)\div 5\left( 2y+7 \right)$.

Answer 1

Hint: Assume the given expression as E. To simplify the expression first take the common factor, which is 3, from the bracket in the numerator. Now, cancel the common expressions, which will be (2y + 7), and factors, which will be 5, of the numerator with that of the denominator to get the answer.

Complete step by step answer:
Here we have been provided with the expression $10y\left( 6y+21 \right)\div 5\left( 2y+7 \right)$ and we are asked to simplify it. Let us see if we have any common factors that can be cancelled. Assuming the given expression as E and converting it into the fractional form we get,
$\Rightarrow E=\dfrac{10y\left( 6y+21 \right)}{5\left( 2y+7 \right)}$
Clearly we can see that we can take 3 common from the terms inside the bracket present in the numerator. So we get,
$\Rightarrow E=\dfrac{10y\times 3\left( 2y+7 \right)}{5\left( 2y+7 \right)}$
We can see that the term (2y + 7) is common in both the numerator and the denominator. Also, we have the factor 5 common in the numerator and the denominator, so cancelling these factors and expressions we get,
$\begin{align}
  & \Rightarrow E=\dfrac{2y\times 3}{1} \\
 & \therefore E=6y \\
\end{align}$
Hence, the simplified form of the given expression is 6y.

Note: Remember the formulas or the laws of exponents because they are used in certain topics of mathematics to simplify the expressions although, they were not of much importance here because we had linear expressions in y. You can apply the long division method also to get the answer however it isn’t needed here because we are easily able to cancel the common factors.