operations with monomials

A. ADDITION AND SUBTRACTION

We can only add or subtract like monomials. Then we add or subtract the coefficients of the monomials and put the same literal part.

Example:

3x + 4x = 7x

5abc² – 4abc² = abc²

x + x² = x + x²

B. MULTIPLICATION

To multiply monomials, we multiply the coefficients and the literal parts (remember how we multiply powers with the same base):

3x · 5x = 3 · 5 · x · x = 15x²

-3b · 2b² = -6b³

To multiply a monomial by an addition, we use the distributive property:

3·(x + 2) = 3·x + 3·2 = 3x + 6

2x·(x + 1) = 2x·x + 2x·1 = 2x² + 2x

Exercise: reduce:

a) x + y + 3x - 2y - 5x + y =

b) x³ -3x + 2x² - 5x + 2x³ - x² + 8x =

c) x + 3 - (2x + 5) + 15x - 8 =

d) a - (b - 3a) + (a + b) - (8a - 9b) =

e) 3x²y · 2xy³ =

f) (-2abc³)·(-3a³b²) =

g) x·(2x + 3) =

h) a·(2a - 3b³) =

Solutions: a) -x; b) 3x³ + x²; c) 14x - 10; d) -3a + 9b; e) 6x³y⁴; f) 6a⁴b³c³; g) 2x² + 3x; h) 2a² - 3ab³