Find the value of , if a = x + y, b = x - y and c = 2x - 1
Given:
a = x + y,
b = x - y,
c = 2x - 1
Formula Used:
(a - b)² = a² + b² - 2ab
Solution:
=> a² + b² + c² - 2ab + 2ac - 2bc
=>(x + y)² + (x - y)² + (2x - 1)² - 2(x + y)(x - y) + 2(x + y)(2x - 1) - 2(x - y)(2x - 1)
=>x² + 2xy + y² + x² - 2xy + y² + 4x² - 4x + 1 - 2(x² - y²) + 4x(2x - 1) - 4y(2x - 1)
=>6x² + 2y² - 4x + 1 - 2x² + 2y² + 8x² - 4x - 8xy + 4y
=>2x² + 4y² - 8x + 5
=>(2x)² + (2y)² - 2×2x×2y + 5
=>(2x - 2y)² + 5
=> (2x + 2y - 1)²
Thus, the correct answer is (b).
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