Subtraction of algebraic expressions OR POLYNOMIALS
Subtraction of like terms :
Ex : i) 5a - 3a = (5 - 3) a = 2a
ii) 3a - 7a = - 4a
iii) - 3a - 6a = (-3 - 6) a = -9a
iv) 3a - (-8a) = 3a + 8a = 11a
v) - 3a - (-8a) = -3a + 8a = 5a
Above examples are different combinations for subtraction of like terms with monomials.
Subtraction of unlike terms:
Horizontal method :
Rule: The expression to be subtracted is first enclosed in brackets with a minus sign prefixed, then on removal of the brackets the like terms are combined.
Ex : Subtract 3a - 2b - c from 4a - 3b + 5c
Sol : 4a - 3b + 5c - (3a - 2b - c)
= 4a - 3b + 5c - 3a + 2b + c
= (4 - 3) a + (-3 + 2) b + (5 + 1) c
= a - b + 6c
Column method :
Rule : Write the expression to be subtracted below the other expression such that the like terms of the two expressions are in the same column, now change the sign of each term of the lower expression and add term wise.
Ex : Subtract 3p - 8q + 5r from 7q + 10p - 3r
Sol : 10p + 7q - 3r
3p - 8q + 5r
- + -
7p + 15q - 8r