Question

Simplify :
(x + y + z) ² + (x + y/2 + z/3 )² - (x/2 + y/3 + z/4 )²

Answer 1

Step-by-step explanation:

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

[ x² + y² + z² + 2xy + 2yz + 2xz] + [x² + y²/4 + z²/9 + xy + yz/3 + zx²/3]

-[x²/4 + y²/9 + 2²/16 + xy/3 + yz/6 + xz/4]

x²+ y² + z² + 2xy + 2yz + 2 × z + x² + y²/y + z²/9

xy + y²/3 + 2x²/3 - x²/y - y²/9 + -2²/9 - xy - yz/6 - xz/u

x² + x² -x²/y + y² + y²/y - y²/9 + z² + 2²/9 -2²/16 + 2xy + xy - y/3 + 2yz + y²/3 + 2xz + 2x²/3 - X2/4

x² + x² - x²/6 = 7x²/4 y² + y²/4 - y²= 3y²+ 9y/36 - 44y²

= 4/y² /36

z² + 2²/9 - 2²/16 = 1442²+ 162²- 92² = 1512²/144

2xy + xy/3 = 6xy + 3xy - 1/3

= 8xy /3

2y2 + y2/3 - ye/6 = 1242 + 242 - 42 /6 = 1342 /6

2× 2 2 2/3 + x²/4 = 24x²+ 8 × 2 - 3 × 2 = 29× 2/4

= 8x²/4 + 414²/36 + 512/144 + 84y + 134²/6 + 29x²/4