Home Real Numbers Radicals Inequalities & Absolute Value Polynomials Rational Expressions 1 Rat'l. Exp. 2 - mult&div Rat'l. Exp. 3 - add&subt Slope & Equations of Lines Review&Test

### UNIT 1  : PRECALCULUS PREP

LESSON 4:  OPERATIONS WITH POLYNOMIALS

Example 1: “+” sign preceding brackets – simply drop the brackets and collect like terms

a)  (3x2 – 2x + 5) + (5x2 – 3x – 6) = 3x2 – 2x + 5 + 5x2 – 3x – 6                                ** drop brackets

= 3x2 + 5x2 –2x – 3x +5 – 6                                  ** Collect like terms

= 8x2 – 5x – 1

Example 2: “-” sign preceding brackets – multiply each term in the bracket by “-1” and collect like terms

(5x2 – 3x + 6) – (2x2 – 7x + 8) = (5x2 – 3x + 6) – 1(2x2 – 7x + 8)                              ** multiply 2nd bracket by “-1”

= 5x2 – 3x + 6 – 2x2 + 7x - 8

= 5x2 – 2x2 – 3x + 7x + 6 – 8                                     ** collect like terms

= 3x2 + 4x - 2

Example 3:

a)  (7a2 – 3ab – 5b2) + ( 4a2 – 8ab – 2b2) = 7a2 – 3ab – 5b2 + 4a2 – 8ab – 2b2

= 7a2 + 4a2 – 3ab – 8ab – 5b2 – 2b2

= 11a2 – 11ab – 7b2

b) (8x + 3y – 5xy) – (4x – 7y – 6xy) = (8x + 3y – 5xy) – 1(4x – 7y – 6xy)                  ** multiply 2nd bracket by “-1”

= 8x + 3y – 5xy – 4x + 7y + 6xy

= 8x – 4x + 3y + 7y – 5xy + 6xy                        ** collect like terms

= 4x + 10y + xy

Multiplying with Polynomials (Expanding):

Example 1: Monomial x Polynomial – multiply each term in bracket by the monomial

a) –3x(2x2 – 5x + 7) = -3x(2x2) – 3x(-5x) – 3x(7)                                                       ** multiply each term by “-3x”

= -6x3 + 15x2 – 21x

b)  2x(5x – 3) –5(2x + 7) = 10x2 – 6x – 10x – 35                                                        ** multiply each term in 1st bracket by “2x” and 2nd bracket by “-5”

= 10x2 – 16x – 35                                                               ** collect like terms

Example 2: Polynomial x Polynomial – multiply each term in 1st  bracket by each term in 2nd  bracket

a) (3x + 5)(2x – 7) = 3x(2x – 7) + 5(2x – 7)                                                                 ** multiply each term in 1st  bracket by each term in 2nd  bracket

= 6x2 – 21x + 10x –35                                                                   ** expand as in previous example

b) (2x + 3)(3x2 – 5x – 2) = 2x(3x2 – 5x – 2) + 3(3x2 – 5x – 2)                                     ** multiply each term in 1st  bracket by each term in 2nd  bracket

= 6x3 –10x2 – 4x + 9x2 –15x – 6                                           ** expand

= 6x3 – x2 –19x – 6                                                               ** collect like terms

c) 2(5x – 3)2 – 3(2x – 1)(3x + 2) = 2(5x – 3)(5x – 3) – 3(2x – 1)(3x + 2)

= 2(25x2 – 15x – 15x + 9) – 3(6x2 + 4x – 3x – 2)

= 50x2 – 30x – 30x + 18 – 18x2 – 12x + 9x + 6

= 32x2 – 63x  + 24