Algebra of Bhaskara II

Minuend = 3n³ + 2p² — 7y³
Subtrahend = 5n³ — p² + y³ — 3y·k
Difference = — 2n³ + 3p² — 8y³ + 3y·k.

(4) Simplify 2y — [ 3y + { 4k — ( 2y — k ) + 5y } — 7k ].

The given expression =
2y — [ 3y + { 4k + 2y — k — 5y } — 7k ] =
2y — [ 3y + { 5k + 3y } — 7k ] =
2y — [ 3y + 5k + 3y — 7k ] =
2y — ( 6y — 2k ) = 2y — 6y + 2k = — 4y + 2k.

Practice Examples:

(1) Find the value of — y + k — n + p,
y + 2k — 4n + 16p + l,
8y + 6n — 2k — 2p + 2l + h.
Given y = 2, k = 3, n = 8, p = 3, l = 5, h = 1.

(2) Find the value of y — k — ( — n ) + p,
— ( — y ) — k — n — ( — l ),
— y — ( — k — n ) + p — ( — n + h ).
Given y = 3, k = 2, n = 4, p = 7, l = 12, h = 10.

(3) Subtract — y + k — n from 2y + 3k — 4n.
(4) Subtract — 3y² + 2y·k — 7k² from y² — 5y·k — 8k².
(5) Subtract y⁴ — 7y² + 6 from 3y⁴ — 2y³ — 8y² + 7.
(6) Subtract — 5y⁵ + 2y⁴ + y³ + 6y² + 6y + 8 from y⁵ — 6y⁴ — 4y² + 5.
(7) Subtract 8y³ — 7y².k + 10y.k² — 13y.k³ + 5k³ from 5y⁴ — 12y³.k + 4y².k² — 23y.k³ + 3k⁴.
(8) Subtract 37y⁶ — 28y⁵.k + 43y⁴.k² — 54y³.k³ — 67y².k⁴ + 84y.k⁵ — 63k⁶ from 48y⁶ — 31y⁵.k — 7y⁴.k² — 36y³.k³ — 41y².k⁴ + 65y.k⁵ — 43k⁶.

The Rule for Multiplication:

The product of two positives or two negatives is positive. The product of a positive and a negative is negative. This rule applies even in division.