Question

(2m-8n)2+(2m+8n)2 simplify​

Answer 1

(2m-8n)²+(2m+8n)²

= 4m²+64n²-32mn+4m²+64n²+32mn

= 8m²+128n²

= 8(m² + 16n²)

Answer 2

(2m - 8n)² + (2m + 8n)² = 8m² + 128n²

Given :

The expression (2m - 8n)² + (2m + 8n)²

To find :

Simplify the given expression

Formula :

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is (2m - 8n)² + (2m + 8n)²

Step 2 of 2 :

Simplify the given expression

We use the formula

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

Thus we get

$\sf {(2m - 8n)}^{2} + {(2m + 8n)}^{2}$

$\sf = \{ {(2m)}^{2} - 2 \times 2m \times 8n + {(8n)}^{2} \} + \{ {(2m)}^{2} + 2 \times 2m \times 8n + {(8n)}^{2} \}$

$\sf = (4 {m}^{2} - 32mn + 64 {n}^{2} ) + (4 {m}^{2} + 32mn + 64 {n}^{2} )$

$\sf = 8 {m}^{2} + 128 {n}^{2}$

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