Question

If A = 4x² + y² – 6xy; 

B = 3y² + 12x² + 8xy; 

C = 6x² + 8y² + 6xy then,

 find 

(i) A + B + C 

(ii) (A – B) – C

Answer 1

Given A = 4x² + y² – 6xy; 

B = 3y² + 12x² + 8xy; 

C = 6x² + 8y² + 6xy 

Write the given expressions in standard form. 

A = 4x² – 6xy + y² 

B = 12x² + 8xy + 3y² 

C = 6x² + 6xy + 8y² 

(i) A + B + C = (4x² – 6xy + y²) + (12x² + 8xy + 3y²) + (6x² + 6xy + 8y²) 

= 4x² – 6xy + y² + 12x² + 8xy + 3y² + 6x² + 6xy + 8y² 

= (4x² + 12x² + 6x² ) + (- 6xy + 8xy + 6xy) + (y² + 3y² + 8y² ) 

= (4 + 12 + 6) x² + (- 6 + 8 + 6) xy + (1 + 3 + 8)y² 

∴ A + B + C = 22x² + 8xy + 12y²

(ii) (A – B) – C 

A + (- B) + (- C) 

Additive inverse of B is 

– B = – (12x² + 8xy + 3y² ) 

∴ – B = – 12x² – 8xy – 3y² 

Additive inverse of C is 

– C = -(6x² + 6xy + 8y² ) 

∴ – C = – 6x² – 6xy – 8y² 

A + (- B) + (- C) 

= (4x² – 6xy + y² ) + (- 12x² – 8xy – 3y² ) + (- 6x² – 6xy – 8y²) 

= 4x² – 6xy + y² – 12x² – 8xy – 3y² – 6x² – 6xy – 8y² 

= (4²x – 12x² – 6x² ) + (- 6xy – 8xy – 6xy) + (y² – 3y² – 8y² )

∴ (A – B) – C = – 14x² – 20xy – 10y²