Question

factorise the equation given above by using appropriate identity.........solve it on a paper ,click the pic and just send.......​

Answer 1

Given

2x² + y² + 8z² - 2√2xy + 4√2yz - 8xz

Factories it

Solution

= 2x² + y² + 8z² - 2√2xy + 4√2yz - 8xz

Applying identity (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ac

8 = √2 × 2 × 2 = 2√2

= (-√2x)² + (y)² + (2√2z)² + 2*(-√2x)*y + 2*y*2√2z + 2*(-√2x)*2√2z

= (-√2x + y + 2√2z)²

= (-√2x + y + 2√2z) (-√2x + y + 2√2z)

Important identities

• (a+b)² = a² + b² + 2ab
• (a-b)² = a² + b² - 2ab
• (a+b)³ = a³ + b³ + 3ab(a+b)
• (a-b)³ = a³ - b³ - 3ab(a-b)
• a² - b² = (a+b)(a-b)
• a³ - b³ = (a-b)(a²+ab+b²)
• a³ + b³ = (a+b)(a² -ab +b²)