Question

The product of (4x + y) (4x – y) is​

Answer 1

$\bold{(4x + y) (4x – y)}$

$\bold{4x(4x - y) + y(4x – y)}$

$\bold{16 {x}^{2} - 4xy+ y(4x – y)}$

$\bold{16 {x}^{2} - 4xy+ 4xy – yy}$

$\bold{16 {x}^{2} - 4xy+ 4xy – {y}^{2} }$

$\bold{16 {x}^{2} - {y}^{2}}$

Answer 2

Given: (4x + y)(4x - y)

To find: The product of (4x + y)(4x - y)

Solution:

Expanding the given expression:

⇒ 4x(4x - y) + y(4x - y)

Solving the expression

⇒ 16$x^{2}$ - 4xy + 4xy - $y^{2}$

⇒ 16$x^{2}$ - $y^{2}$                                      [-4xy + 4xy = 0]

⇒ $(4x)^{2} - y^{2}$

Therefore, the required product is  $(4x)^{2} - y^{2}$ .

                                           

                                                           OR

The given expression can also be solved using the algebraic identity :-

.: $a^{2} - b^{2}$ = (a + b)(a - b)

Now, you can observe that the given expression (4x + y)(4x - y) is in the form of (a + b)(a - b).

Hence, (4x + y)(4x - y) = $(4x)^{2} - y^{2}$.