Question

Multiply the expressions - $\left( a+7 \right)$ and $\left( b-5 \right)$?

Answer 1

Hint: Assume the required expression as ‘E’. Now, to multiply the two binomial terms by considering the product of the terms present in both of them systematically. First multiply the first term which is ‘a’ in $\left( a+7 \right)$ with the two terms in $\left( b-5 \right)$ one by one using proper signs. Similarly, multiply the second term which is 7 in $\left( a+7 \right)$ with the two terms in $\left( b-5 \right)$ one by one to get the answer.

Complete step-by-step solution:
Here we have been provided with two binomials $\left( a+7 \right)$ and $\left( b-5 \right)$ and we are asked to multiply them. Let us assume this product as ‘E’, so we have,
$\Rightarrow E=\left( a+7 \right)\left( b-5 \right)$
Now, we need to multiply each term in the first expression $\left( a+7 \right)$ with each term in the second expression $\left( b-5 \right)$ one by one to get the product. So let us proceed systematically and find the product. First we will multiply ’a’ present in $\left( a+7 \right)$ with the two terms present in $\left( b-5 \right)$ and further we will multiply 7 present in $\left( a+7 \right)$ with the two terms present in $\left( b-5 \right)$ to get the answer. So we get,
$\begin{align}
  & \Rightarrow E=a\left( b-5 \right)+7\left( b-5 \right) \\
 & \therefore E=ab-5a+7b-35 \\
\end{align}$
Hence, the above expression is our answer.

Note: You may check the answer by assigning any particular value to the variables ‘a’ and ‘b’. In these types of questions you must be careful about the sign between the two terms. Remember the algebraic relations: $\left( -1 \right)\times 1=-1$ and $\left( -1 \right)\times \left( -1 \right)=1$ to simplify the expression. Proceed serially while taking the product otherwise you may get confused in the multiplication of multiple terms.