Add, Subtract and Multiply Polynomials

I. To add two polynomials, group the like terms in column form and add the like terms.

(3x² - 7x + 9) + (- 2x² - 8x + 3) =

(3x² - 7x + 9)

- 2x² - 8x + 3)

 x² - 15x + 12)

II. To subtract two polynomials, group the like terms in column form and subtract the like terms. You can also use the inverse of the second polynomial and add the like terms.

(5x² - 8x + 12) - ( 3x² - 2x + 6) =

(5x² - 8x + 12)

- ( 3x² - 2x + 6)

- 3x² + 2x - 6     (Use the inverse and then add the terms)

  2x² - 6x + 6)

III.  To multiply a polynomial by a monomial, multiply each term in the polynomial by the monomial.

(5x² - 8x + 12) ( - 3 x³ ) = -15x⁵ + 24x⁴  - 36x³ 

 

IV. To multiply two polynomials, multiply each term in the second polynomial by each term in the first polynomial (distributive property), and then combine like terms.

(5x² - 8x + 12) - ( 3x² - 2x + 6) =

5x² ( 3x² - 2x + 6) + 8x ( 3x² - 2x + 6) + 12( 3x² - 2x + 6) =

15x⁴ - 10x³  + 30x² + 24x³  - 16x² + 48x + 36x² - 24x +72 =

 15x⁴ + 14x³  + 50x² + 8x + 36x² + 24x +72

V. Special Products:

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

(a + b)(a - b) = a² - b²