Operations on Polynomials

Operations on Polynomials

• Addition, subtraction, multiplication, and division of polynomials follow similar rules as algebraic expressions.

Subtraction Example

• To subtract polynomials, rearrange and combine like terms.
• Example calculation:
  • Subtract (5a^2 - 2a) from (7a^2 + 5a + 6) results in:
  • ( (7a^2 + 5a + 6) - (5a^2 - 2a) = 2a^2 + 7a + 6 )

Multiplication Example

• To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial.
• Example calculation:
  • Multiply (-2a) by (5a^2) yields:
  • (-2a \times 5a^2 = -10a^3)

Polynomial Product Example

• Multiplying two polynomials requires distributing each term in one polynomial by each term in the other.
• Example calculation:
  • For ((m^2 - 5) \times (m^3 + 2m - 2)):
  • Distributing gives:
    • ( m^5 + 2m^3 - 2m^2 - 5m^3 - 10m + 10 )
  • Combining like terms results in:
    • ( m^5 - 3m^3 - 2m^2 - 10m + 10 )
  • Degree of the resulting polynomial is 5.

Addition Example

• Adding polynomials involves rearranging and combining like terms.
• Example calculation:
  • Adding (3m^2n + 5mn^2 - 7mn) and (2m^2n - mn^2 + mn):
  • Results in:
    • ( 5m^2n + 4mn^2 - 6mn ) after arranging and combining like terms.