Question

Factorise the following: 

(i) 4x² + 9y² + 25z² + 12xy + 30yz + 20xz 

(ii) 25x² + 4y² + 9z² – 20xy + 12yz – 30xz

Answer 1

(i) 4x² + 9y² + 25z² + 12 xy + 30 yz + 20 xz 

= (2x)² + (3y)² + (5z)² + 2(2x)(3y) + 2(3y) + (5z) + 2 x 3y x 5z 

= (2x + 3y + 5z)² 

∵ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

(ii) 25x² + 4y² + 9z² – 20xy + 12yz – 30xz

= (5x)² + (-2y)² + (-3z)² + 2(5x)(-2y) + 2(-2y)(-3z) + 2(-3z)(5x) 

= (5x – 2y – 3z)²