Algebra of Bhaskara II

3 + 4 = 7,
4 — 3 = 1,
3 — 4 = — 1.

New examples for finding the sum:

(1) Find the sum of — y — k·n, y²·k,
given that y = 4, k = 2, n = 5.
Therefore, { ( — 4 — 2 × 5 ) + 4² × 2 } =
{ ( — 4 — 10 ) + 16 × 2 } =
— 14 + 32 = 18.

(2) What is the meaning of ( — 3 n ) + ( — y³·p ) + ( y + k + n )?
Given that y = 1, k = 2, n = 3, p = 4.
Therefore, ( — 3 × 3 ) + ( — 1³ × 4 ) + ( 1 + 2 + 3 ) =
( — 9 ) + ( — 4 ) + ( 6 ) = — 13 + 6 = — 7.

(3) What is the value of y³·k — y²·n + p·n² — k²·n?
Given that y = 2, k = 4, n = 6, p = 8.
Therefore, 2³ × 4 — 2² × 6 + 8 × 6² — 4² × 6 =
8 × 4 — 4 × 6 + 8 × 36 — 16 × 6 =
32 — 24 + 288 — 96 = 8 + 288 — 96 =
296 — 96 = 200.

(4) Tell the sum of ( 3y — 2k + n ) and ( — 5p + 6p — n ),
given that y = 2, k = 7, n = 3, p = 1.
( 3 × 2 — 2 × 7 + 3 ) + ( 5 × 1 + 6 × 1 — 3 ) =
6 — 14 + 3 + 5 + 6 — 3 =
( 6 + 3 + 5 + 6 ) + ( — 14 — 3 ) = 20 — 17 = 3.

Practice Examples:

(1) Add — 14, — 25, and — 10.
(2) Find the value of — y + ( k² + n ),
given that y = 2, k = 15, and n = 30.