algebraic expression

Question

 Show that: (5xy+3y)² -(5xy-3y)²=60xy²

 

Answer 1

 (5xy+3y)² -(5xy-3y)²=60xy² 

 

Look at the formulas for the sum and difference of two squares:

(a+b)² = a² + 2ab + b²

(a-b)² = a² - 2ab + b²

 

(a+b)² - (a-b)² = (a² + 2ab + b²) - (a² - 2ab + b²) = 4ab

 

For your problem a=5xy, b = 3y

 

4ab = 4(5xy)(3y) = 60xy²

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If you wish to multiply these out the long way and subtract

them you have:

 

  (5x+3y)² = 25x² + 30xy² + 9y²

-(5x-3y)² = -(25x² - 30xy² + 9y²)

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                              60xy²

Answer 2

Did you try to use the formula a^2 - b^2 = (a+b)*(a-b) ?