Question

Simplify using suitable identity : (3x + 5y)^2 − (3x − 5y)^2

Answer 1

$\sf \: {(3x + 5y)}^{2} - {(3x - 5y)}^{2}$

Use (a + b)² = a²+ 2ab + b² ,

( a - b)² = a² - 2ab + b²

${9x}^{2} + 30xy + {25y}^{2} - ( {9x}^{2} + 30xy + {25y}^{2} )$

Change the sign of each term after removing brackets.

${9x}^{2} + 30xy + {25y}^{2} - {9x}^{2} + 30xy - 25 {y}^{2}$

Since two opposite becomes zero, cancel the terms.

$\cancel {9x}^{2} + 30xy + \cancel {25y}^{2} \cancel{- {9x}^{2} }+ 30xy \: \: \: \cancel{- 25 {y}^{2} }$

Collect like terms and add them.

$30xy + 3xy$

$\sf \green{= 60xy}$

Answer 2

Answer:

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