CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

(a-b)^2 Expansion and Visualisation

Simplify: 7m-...

Question

Simplify: ${(7 m - 8 n)}^{2} + {(7 m + 8 n)}^{2}$ .

Open in App

Solution

Step 1. Expand ${(7 m - 8 n)}^{2}$ .
Expand the term ${(7 m - 8 n)}^{2}$ :
$\begin{matrix} {(7 m - 8 n)}^{2} = {(7 m)}^{2} + {(8 n)}^{2} - 2 (7 m) (8 n) \\ = 49 m^{2} + 64 n^{2} - 112 m n \end{matrix}$
Step 2: Expand ${(7 m + 8 n)}^{2}$ .
Expand the term ${(7 m + 8 n)}^{2}$ :
$\begin{matrix} {(7 m + 8 n)}^{2} = {(7 m)}^{2} + {(8 n)}^{2} + 2 (7 m) (8 n) \\ = 49 m^{2} + 64 n^{2} + 112 m n \end{matrix}$
Step 3. Simplify ${(7 m - 8 n)}^{2} + {(7 m + 8 n)}^{2}$ .
Add the expanded terms of ${(7 m - 8 n)}^{2} + {(7 m + 8 n)}^{2}$ :
$\begin{matrix} {(7 m - 8 n)}^{2} + {(7 m + 8 n)}^{2} = [49 m^{2} + 64 n^{2} - 112 m n] + [49 m^{2} + 64 n^{2} + 112 m n] \\ = 98 m^{2} + 128 n^{2} \end{matrix}$
Hence, the value of the given expression is ${(7 m - 8 n)}^{2} + {(7 m + 8 n)}^{2} = 41 m^{2} + 41 n^{2} + 80 m n$

Suggest Corrections

thumbs-up

30

Similar questions

Simplify:

.

\sqrt[4]{81 x^{8} y^{4} z^{16}}

{(\frac{3125}{243})}^{\frac{4}{5}}

\frac{32 m^{2} n^{3} p^{2}}{4 m n p}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

(a-b)^2 Expansion and Visualisation

MATHEMATICS

Watch in App

explore_more_icon

Explore more

(a-b)^2 Expansion and Visualisation

Standard VII Mathematics

Join BYJU'S Learning Program

CrossIcon