Question

$simplify \: \: (4x + 5y) 2 - (4x - 5 {y}^{2} )$
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Answer 1

Answer:

80xy

Step-by-step explanation:

1. Expand the square

(4x + 5y)²  - 1(4x – 5y)²  

(4x + 5y) (4x + 5y) - 1(4x – 5y)²

    2. Distribute

(4x + 5y) (4x + 5y) - 1(4x – 5y)²

4x(4x + 5y) + 5y(4x + 5y) - 1(4x – 5y)²

    3. Distribute

4x(4x + 5y) + 5y(4x + 5y) - 1(4x – 5y)²

16x² + 20xy + 5y(4x + 5y) - 1(4x – 5y)²

   4. Distribute

16x² + 20xy + 5y(4x + 5y) - 1(4x – 5y)²

16x² + 20xy +20xy + 25y²- 1(4x – 5y)²

  5. Combine like terms

16x² + 20xy + 20xy + 25y²- 1(4x – 5y)²

16x² + 40xy + 25y²- 1(4x – 5y)²

  6. Expand the square

16x² + 40xy + 25y²- 1(4x – 5y)²

16x² + 40xy + 25y²- 1 (4x – 5y) (4x – 5y)

  7. Distribute

16x² + 40xy + 25y²- 1 (4x – 5y) (4x – 5y)

16x² + 40xy + 25y²- 1{4x (4x – 5y) 5y(4x – 5y)}

  8. Distribute

16x² + 40xy + 25y²- 1{4x (4x – 5y) 5y(4x – 5y)}

16x² + 40xy + 25y²- 1{16x²-20xy-5y(4x-5y)}

  9. Distribute

16x² + 40xy + 25y²- 1{16x²-20xy-5y(4x-5y)}

16x² + 40xy + 25y²- 1{16x²-20xy-20xy+25y²)

 10. Combine like terms

16x² + 40xy + 25y²- 1{16x²-20xy-20xy+25y²)

16x² + 40xy + 25y²- 1(16x²-40xy-25y²)

 11. Distribute

16x² + 40xy + 25y²- (16x²-40xy-25y²)

16x² + 40xy + 25y² - 16x² + 40xy + 25y²

 12. Combine like terms

16x² + 40xy + 25y² - 16x² + 40xy + 25y²

40xy + 25y² + 40xy - 25y²

13. Combine like terms

40xy + 25y² + 40xy - 25y²

80xy +  25y² - 25y²

14. Combine like terms

80xy +  25y² - 25y²

SOLUTION = 80xy