Question

Factorize the following :
i) 4a4 + b4. ii) x3 + 64y3 + z3-12xyz . iii) x3 + 64
iv) 5x2 – 13x – 6

Answer 1

Answer:

$\huge\underline\mathscr{Answers\::}$

1) 4a⁴ + b⁴

➪ (2a²)² + (b²)²

➪ (2a² + b²)² - 2 × a² × b²

➪ (2a² + b²)² - 2a²b²

➪ (2a² + b²)² - (2ab)²

➪ (2a² + b² + 2ab) (2a² + b² - 2ab)

➪ (2a² + 2ab + b²) (2a² - 2ab + b²)

∴ The answer of this question is

(2a² + 2ab + b²) (2a² - 2ab + b²)

Formula used :-

➪ a² + b²

➭ (a + b)² - 2ab

➪ a² - b²

➭ (a + b) (a - b)

2) x³ + 64y³ + z³ - 12xyz

➪ (x)³ + (4y)³ + (z)³ - 3 × x × 4y × z

➪ (x + 4y + z) {(x)² + (4y)² + (z)² - x × 4y - 4y × z - z × x}

➪ (x + 4y + z) (x² + 16y² + z² - 4xy - 4yz - xz)

∴ The answer of this question is

(x + 4y + z) (x² + 16y² + z² - 4xy - 4yz - xz)

Formula used :-

➪ a³ + b³ + c³ - 3abc

➭ (a + b + c) (a² + b² + c² - ab - bc - ca)

3) x³ + 64

➪ (x)³ + (4)³

➪ (x + 4) {(x)² - x × 4 + (4)²}

➪ (x + 4) (x² - 4x + 16)

∴ The answer of this question is

(x + 4) (x² - 4x + 16)

Formula used :-

➪ x³ + y³

➭ (x + y) (x² - xy + y²)

4) 5x² - 13x - 6 = 0

➪ 5x² - (15 - 2)x - 6 = 0

➪ 5x² - 15x + 2x - 6 = 0

➪ 5x(x - 3) + 2(x - 3) = 0

➪ (x - 3) (5x + 2) = 0

➪ (x - 3) = 0

➪ x - 3 = 0

➪ x = 3

Either,

➪ (5x + 2) = 0

➪ 5x + 2 = 0

➪ 5x = - 2

➪ x = - 2/5

∴ The answer of this question is

x = 3, - 2/5