Question

Factorise
100x2 -20x +1

Answer 1

Given

100x² - 20x + 1

Factorise it

Solution

→ 100x² - 20x + 1

★ Solve this by splitting middle term

→ 100x² - 10x - 10x + 1

→ 10x(10x - 1) - 1(10x - 1)

→ (10x - 1)(10x - 1)

Some identities

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• a² - b² = (a + b)(a - b)
• a³ - b³ = (a - b)(a² + ab + b²)
• a³ + b³ = (a + b)(a² - ab + b²)

Answer 2

➲ Fᴀᴄᴛᴏʀɪsᴇ :-

❶ By splitting middle term

➭ 100x² - 20x + 1 = 0

➭ 100x² - 10x - 10x + 1 = 0

➭ 10x ( 10x - 1) - 1 ( 10x - 1) = 0

➭ (10x - 1)( 10x - 1) = 0

➭ x = 1/10 or x = 1/10

❷ By using Identity

➢ (a - b) ² = a² - 2ab + b²

➭ 100x² - 20x + 1 = 0

➭ (10x) ² - 2 × 10x × 1 + 1 = 0

➭ (10x - 1)² = 0

➭ 10x - 1 = 0

➭ x = 1/10