Question

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Answer 1

Answer:

2) (x - 2)(x + 1)(x - 3)(x + 2)

3) I) -(5/9)

ii) 1/7

Step-by-step explanation:

2)

(x² - x)² - 8(x² - x) + 12

Let (x² - x) be p

=> p² - 8p + 12

=> p² - 6p - 2p + 12

=> p(p - 6) - 2(p - 6)

=> (p - 2)(p - 6)

=> (x² - x - 2)(x² - x - 6)

Consider x² - x - 2

=> x² + x - 2x - 2

=> x(x + 1) - 2(x + 1)

=> (x - 2)(x + 1)

Consider x² - x - 6

=> x² + 2x - 3x - 6

=> x(x + 2) - 3(x + 2)

=> (x - 3)(x + 2)

Therefore,

(x² - x)² - 8(x² - x) + 12 = (x - 2)(x + 1)(x - 3)(x + 2)

3)

a/b = 2/3

I) (a² - b²)/b²

=> (a²/b²) - 1

=> (a/b)² - 1

=> (2/3)² - 1

=> (4/9) - 1

=> -(5/9)

ii) (3a² - b²)/(3a² + b²)

Dividing both numerator and denominator by b²

=> ((3a² - b²)/b²) / ((3a² + b²)/b²)

=> (3(a²/b²) - 1) / (3(a²/b²) + 1)

=> (3(a/b)² - 1) / (3(a/b)² + 1)

=> (3(2/3)² - 1) / (3(2/3)² + 1)

=> (3(4/9) - 1) / (3(4/9) + 1)

=> ((4/3) - 1) / ((4/3) + 1)

=> (1/3) / (7/3)

=> 1/7