Question

How do you multiply (4x – 1) (4x + 1)?

Answer 1

Hint: We will first mention the formula $(a - b)(a + b) = {a^2} - {b^2}$, then replace a by 4x and b by 1. Thus, we have the multiplied answer and then we will verify it by normal multiplication.

Complete step by step solution:
We are given that we are required to multiply (4x – 1) (4x + 1).
Now, we know that we have an identity given by the following mentioned formula:-
$ \Rightarrow (a - b)(a + b) = {a^2} - {b^2}$
Now, let us just replace a by 4x and b by 1 in the above mentioned formula, we will then obtain the following expression with us:-
$ \Rightarrow (4x - 1)(4x + 1) = {(4x)^2} - {1^2}$
Simplifying the right hand side of the above mentioned expression, we will then obtain the following expression with us:-
$ \Rightarrow (4x - 1)(4x + 1) = 4x \times 4x - 1 \times 1$
Simplifying the right hand side of the above mentioned expression further, we will then obtain the following expression with us:-
$ \Rightarrow (4x - 1)(4x + 1) = 16{x^2} - 1$
Thus, we have the required answer.

Note: The students must note that the identity we used can be avoided and we can use the direct multiplication to find the answer by using the fact that (a + b) (c + d) = a (c + d) + b (c + d)
Replacing a by 4x, b by – 1, c by 4x and d by 1, we will then obtain the following expression:-
$ \Rightarrow $(4x – 1) (4x + 1) = 4x (4x + 1) – 1 (4x + 1)
Simplifying the calculations on the right hand side, we will then obtain the following expression with us:-
$ \Rightarrow (4x - 1)(4x + 1) = 16{x^2} + 4x - 4x - 1$
Clubbing the like terms in the right hand side of the above mentioned equation, we will then obtain the following expression:-
$ \Rightarrow (4x - 1)(4x + 1) = 16{x^2} - 1$
Thus, we have the required answer.