Q. 4 a) If a = x+y and b = x-y, show that I) (a+b) ² = 4x² ii) (a-b) ² = 4y²

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Mathematics

4 November, 19:04

Q. 4 a) If a = x+y and b = x-y, show that I) (a+b) ² = 4x² ii) (a-b) ² = 4y²

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Anya Pruitt · Answer 1

Below.

Step-by-step explanation:

i) (a + b) ^2 = a^2 + 2ab + b^2

= (x + y) ^2 + 2 (x + y) (x - y) + (x - y) ^2

= x^2 + 2xy + y^2 + 2 (x^2 - y^2) + x^2 - 2xy + y^2

= x^2 + 2x^2 + x^2 + y^2 - 2y^2 + y^2 + 2xy - 2xy

= 4x^2.

ii) (a - b) ^2 = a^2 + b^2 - 2ab

= (x + y) ^2 + (x - y) ^2 - 2 - 2 (x^2 - y^2)

= x^2 + 2xy + y^2 + x^2 - 2xy + y^2 - 2x^2 + 2y^2

= x^2 + x^2 - 2x^2 + y^2 + y^2 + 2y^2 + 2xy - 2xy

= 4y^2.