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It is given thatopen parenthesis, x minus 2y, close parenthesis, times open parenthesis, x + 2y, close parenthesis, = 4Quantity A: x squared, minus, 4 times the quantity y squared Quantity B: 8 A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.

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sqdancefan

Answer:

  Quantity B is greater.

Explanation:

Given:

  (x -2y)(x +2y) = 4

  A = x² -4y²

  B = 8

Find:

  the relationship between A and B

Solution:

The given expression can be expanded to give ...

  x(x +2y) -2y(x +2y) = x² +2xy -2xy -4y² = x² -4y²

This is precisely the expression designated as A. Its value is 4.

  4 < 8

  A < B

Quantity B is greater.