Exercise Make up a fifth-degree monomial with two variables. Example: 3x 4y
Exercise Make up a third-degree trinomial with one variable. Example: 7x 3 + 5x2 – 4
Exercise Make up a ninth-degree binomial with three different variables. Example: 4x 5y 3z + 2xy
Exercise Make up a monomial with a degree of zero. Example: 15
Exercise Make up a second-degree binomial with three variables. Example: 7xy – 2z
Like Terms Like terms are terms that contain an identical variable or variables all raised to the same respective powers.
To add polynomials, add like terms using the Commutative, Associative and Distributive Properties.
Commutative Property addition: a + b = b + a multiplication: ab = ba
Associative Property addition: a + (b + c) = (a + b) + c multiplication: a(bc) = (ab)c
Distributive Property a(b + c) = ab + ac
Example 1 Add (3x + 4) + (2x – 6). (3x + 4) + (2x – 6)
Example 2 Add (– 5y + 9z) + (– y – 5z). (– 5y + 9z) + (– y – 5z) (– 5y – y) + (9z – 5z) (– 5 – 1)y + (9 – 5)z – 6y + 4z
Example Add (3x + 4y) + (2x – 2y). 5x + 2y
Example Add (3x + 2) + (4x – 7). 7x – 5
Example Add (4xy + 3x – 1) + (– 3xy + 4y + 2). xy + 3x + 4y + 1
Example 3 Add (3x2 – 10x + 9) + (– 8x2 + 17x – 2).
Example 4 Add (3a3 – 8a – 9) + (5a3 + 10a2 + 8).
Example Add (3x2 + 4x – 2) + (– 7x2 + 3x + 1). – 4x2 + 7x – 1
Example Add (4x2 + 3x – 8) + (11x2 – 5x + 8). 15x2 – 2x
Example Add (7x 5 + 3x 4 – 2x2 + 3x + 1) + (4x 4 – 3x 3 + 2x – 5).
Example Add (3x + 7 – x 3) + (2x 3 + 1 – 4x). x3 – x + 8
Example Add (3x 6 + 4x 4 – 2x + 4x2 + x 3 – 1) + (7x 6 + 4x2 – 5 + 7x 3). 10x 6 + 4x 4 + 8x 3 + 8x2 – 2x – 6
Example Add (5x2 – 4x – 3) + (2x2 + 8) + (4x – 7). 7x2 – 2
Example 5 Add (2.5x2 + 8.2xy – 4y2) + (3x2 – 0.4xy – 1.5y2). (2.5x2 + 3x2) + (8.2xy – 0.4xy) + (– 4y2 – 1.5y2) 5.5x2 + 7.8xy – 5.5y2
Example 6 1 5 3 10 1 10 3 5 Add x + + x – . 1 5 3 10 1 10 3 5 x + + x – 1 5 1 10 3 10 3 5 x + x + –
Example 6 1 5 3 10 1 10 3 5 Add x + + x – . x + x + – 2 10 1 10 3 10 6 10 3 10 x – or 0.3x – 0.3
Example Add (3.5x2 + 1.27x + 5.3) + (4.9x2 – 3.53x + 1.8).