Question

How do you multiply $ (3x - 7)(5x + 6) $ ?

Answer 1

Hint: To solve this problem we should know how to multiply exponent.
Exponent formula: An exponential function is defined as a function with a positive constant other than 1 raised to a variable exponent.
Some, exponent formula:
I. $ {x^n} \times {x^m} = {x^{m + n}} $
II. $ \dfrac{{{x^m}}}{{{x^n}}} = {x^{m - n}} $

Complete step by step solution:
As given in question, $ (3x - 7)(5x + 6) $ .
We have to multiply $ (3x - 7) $ by $ (5x + 6) $ .
So, can write it as, $ (3x - 7)(5x + 6) $
  $ = (3x - 7)5x + (3x - 7)6 $
We will multiply $ (3x - 7)5x $ . we get,
  $ = 3x \times 5x - 7 \times 5x $
By using $ {x^n} \times {x^m} = {x^{m + n}} $
  $ = 15{x^2} - 35x $ …………………. $ (1) $
We will multiply $ (3x - 7)6 $ . we get,
  $ = 3x \times 6 - 7 \times 6 $
  $ = 18x - 42 $ …………………………… $ (2) $
Add $ (1) $ and $ (2) $ . We get,
 \[(3x - 7)5x + (3x - 7)6 = 15{x^2} - 35x + 18x - 42\]
Solving it further. We get,
 \[ \Rightarrow 15{x^2} - 35x + 18x - 42 = 15{x^2} - 17x - 42\]
Hence,
  $ (3x - 7)(5x + 6) = 15{x^2} - 17x - 42 $
So, the correct answer is “ $ (3x - 7)(5x + 6) = 15{x^2} - 17x - 42 $”.

Note: To check our calculation is correct or not. We will use trial and error method:
Let’s keep $ x = 1 $ to check our answer.
Put it in equation: $ (3x - 7)(5x + 6) $
We get, $ (3x - 7)(5x + 6) = (3 \times 1 - 7)(5 \times 1 + 6) $
  $ \Rightarrow (3 \times 1 - 7)(5 \times 1 + 6) = - 4 \times 11 = - 44 $ …………………. $ (1) $
Put in equation $ 15{x^2} - 17x - 42 $
We get, $ 15{x^2} - 17x - 42 = 15 \times {1^2} - 17 \times 1 - 42 $
  $ \Rightarrow 15 \times {1^2} - 17 \times 1 - 42 = 15 - 17 - 42 = - 44 $ …………………………… $ (2) $
Hence, $ (1) $ and $ (2) $ are equal. So, our calculation is right.