Question

(8n - 7m)^2 - (7m -8n)^2​

Answer 1

Answer:

$(8n - 7m)^2 - (7m -8n)^2 =0$

Step-by-step explanation:

$(8n - 7m)^2 - (7m -8n)^2​ \\=[(8n)^2 - 2 (8n)(7m) + (7m)^2] - [(7m)^2 - 2(7m)(8n) + (8n)^2]\\=[64n^2 - 112 nm + 49m^2] - [49m^2 - 112mn + 64n^2]\\ =64n^2 - 112 nm + 49m^2 - 49m^2+ 112mn - 64n^2\\=64n^2 - 64n^2 - 112 nm +112 nm+ 49m^2 - 49m^2\\=0$

Answer 2

Given: The equation is$(8 n-7 m)^{2}-(7 m-8 n)^{2}$.

We have to solve the above equation.

By using the identity rule, we are solving the above equation.

As we know that$a^{2}-b^{2}=(a+b)(a-b)$.

We are solving in the following way:

Here,

$a=8 n-7 m \text \ \ and\ \ b=7 m-8 n \text {. }$

We have,

The equation is$(8 n-7 m)^{2}-(7 m-8 n)^{2}$

$\begin{array}{l}=[(8 n-7 m)+(7 m-8 n)][(8 n-7 m)-(7 m-8 n)] \\\\=[8 n-7 m+7 m-8 n][8 n-7 m-7 m+8 n] \\\\=[0][16 n-14 n] \\\\=0\end{array}$

Hence, the solution of the above equation is$0$.