Factorize: 3x^2 + 4y^2 + 25z^2 - 4√3xy – 20yz + 10√3zx.
Answers
Solution :
3x² + 4y² + 25z² - 4√3 xy - 20 yz + 10√3 xz
=> ( √3 x )² + ( 2y )² + ( 5z )²- 4√3 xy - 20 yz + 10√3 xz
=> ( √3 x )² + ( 2y )² + ( 5z )²- 2 × 2 ×√3 xy - 2 × 2 × 5 yz + 2 × 5√3 xz
=> [ √3x - y + z ]²
The surface plot of this polynomial in the figure above.
Additional Information :
(a + b)² = a² + 2ab + b²
(a + b)² = (a - b)² + 4ab
(a - b)² = a² - 2ab + b²
(a - b)² = (a + b)² - 4ab
a² + b² = (a + b)² - 2ab
a² + b² = (a - b)² + 2ab
2 (a² + b²) = (a + b)² + (a - b)²
4ab = (a + b)² - (a - b)²
ab = {(a + b)/2}² - {(a-b)/2}²
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
(a + b)³ = a³ + 3a²b + 3ab² b³
(a + b)³ = a³ + b³ + 3ab(a + b)
(a - b)³ = a³ - 3a²b + 3ab² - b³
a³ + b³ = (a + b)( a² - ab + b² )
a³ + b³ = (a + b)³ - 3ab( a + b)
a³ - b³ = (a - b)( a² + ab + b²)
a³ - b³ = (a - b)³ + 3ab ( a - b )
