Question

factorise :
(i) (4y² – 1)² – 15(y² – 1) – 4
(ii) (x² – 3x)² – 8(x² – 3x) – 20
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Answer 1

$\huge\bold\green{Answer :-}$

1) (4y² - 1)² - 15(y² - 1) - 4

➪ {(4y²)² - 2 × (4y²) × (1) + (1)²} - 15y² + 15 - 4

➪ 16y⁴ - 8y² + 1 - 15y² + 11

➪ 16y⁴ - 8y² - 15y² + 11 + 1

➪ 16y⁴ - 23y² + 12

∴ The answer of this question is

16y⁴ - 23y² + 12

2) (x² - 3x)² - 8(x² - 3x) - 20

➪ {(x²)² - 2 × x² × 3x + (3x)²} - 8x² + 24x - 20

➪ x⁴ - 6x³ + 9x² - 8x² + 24x - 20

➪ x⁴ - 6x³ + x² + 24x - 20

➪ x⁴ - x³ - 4x² + 4x - 5x³ + 5x² + 20x - 20

➪ x(x³ - x² - 4x + 4) - 5(x³ - x² - 4x + 4)

➪ (x - 5) (x³ - x² - 4x + 4)

➪ (x - 5) {x²(x - 1) - 4(x - 1)}

➪ (x - 5) (x - 1) (x² - 4)

➪ (x - 5) (x - 1) {(x)² - (2)²}

➪ (x - 5) (x - 1) (x + 2) (x - 2)

∴ The answer of this question is

(x - 5) (x - 1) (x + 2) (x - 2)

Formula used :-

➪ (a - b)²

➭ a² - 2ab + b²

➪ a² - b²

➭ (a + b) (a - b)