Question

Find product using the distributive law of multiplication $(x + 7)(x - 2)$

Answer 1

Hint: Distributive law of multiplication is the general arithmetic rule of rearranging the terms present in the given function so as to carry out analysis. Distributive law states that multiplying a number by a group of numbers added or subtracted together is the same as doing each multiplication separately.
Here, in the question, we need to find the product of the function and establish the distributive law in the given function for which we can use the formula $a \times (b \pm c) = ab \pm ac$ to solve the given expression $(x + 7)(x - 2)$. First we have to convert the given expression in the distributed model of $a(b \pm c)$ and then find the product of the resulting function.



Complete step by step solution:
The given function is $(x + 7)(x - 2)$ which can also be written as: $x(x - 2) + 7(x - 2) - - - - (i)$
Now applying the distributive law in the equation (i) as:
$(x + 7)(x - 2) = x(x - 2) + 7(x - 2) - - - - (ii)$
We have to prove that the equation (ii) is true. So,
Carrying the product of the left-hand side of the equation (ii) as:
$
  LHS = (x + 7)(x - 2) \\
   = {x^2} + 7x - 2x - 14 \\
   = {x^2} + 5x - 14 - - - - (iii) \\
 $
Similarly, carrying the multiplication process in the right-hand side of the equation (ii) as:
$
  RHS = x(x - 2) + 7(x - 2) \\
   = {x^2} - 2x + 7x - 14 \\
   = {x^2} + 5x - 14 - - - - (iv) \\
 $
As, we can see from equation (iii) and (iv) that the left-hand side of the equation is equals to the right hand side of the equation i.e., $LHS = RHS$
Hence, the function $(x + 7)(x - 2)$ follows the distributive law.


Note: We can also use the left distributive law by applying the operation i.e., $a \times (b \pm c) = ab \pm ac$. We use various types of laws which come under addition and multiplication i.e. commutative, associative, distributive laws. In our case question concerns about only distributive law i.e. left distributive law.