a) 5 + √x + 25 - x
= (5 + √x) + (25 - x)
= (5 + √x) + (5 - √x)(5 + √x)
= (5 + √x)(1 + 5 - √x)
= (5 + √x)(6 - √x)
b) xy - x√y + √y - 1
= (xy - x√y) + (√y - 1)
= x√y(√y - 1) + (√y - 1)
= (√y - 1)(x√y + 1)
c) √(a - b) - √(a² - b²)
= √(a - b) - √[(a - b)(a + b)]
= √(a - b)[(1 - √(a + b)]
d) √(ax) + √(by) - √(bx) - √(ay)
= [√(ax) - √(bx)] - [√(ay) - √(by)
= √x.(√a - √b) - √y.(√a - √b)
= (√a - √b)(√x - √y)
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