Question

After simplification of the given expression : (6m – 4n)2 + (6m + 4n)2 . which of the following option you will get
(a) 12m² + 8n²
(b) 36m² - 16n²
(c) 72m² + 32n²
(d) 36m² + 16n²- 48mn​

Answer 1

Step-by-step explanation:

By Applying property::

(a+b)² + (a-b)² = 2a²+2b²

Therefore

Answer is 2(6m)² + 2(4n)² = 72m² + 32n²

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Answer 2

Answer:

c)  (6m – 4n)² + (6m + 4n)²= 72m² + 32n²

Step-by-step explanation:

Given: $(6m - 4n)^2 + (6m + 4n)^2$

Formula:

$(a + b)^2 = a^2 + 2ab + b^2\\(a - b)^2 = a^2 - 2ab + b^2$

$(6m - 4n)^2 + (6m + 4n)^2\\=[ (6m)^2 - 2(6m)(4n) + (4n)^2] + [(6m)^2 + 2(6m)(4n) + (4n)^2]\\=36m^2 - 48mn + 16n^2 + 36m^2 +48mn + 16n^2$

Rearrange the similar terms

$= 36m^2 + 36m^2 +48mn - 48mn + 16n^2 + 16n^2\\= (36 + 36)m^2 + (16 + 16)n^2\\= 72m^2 + 32n^2\\= 2 (36m^2 + 16n^2)\\= 2[(6m)^2 + (4n)^2]$