2.1 Adding and Multiplying Polynomials Secondary Math II Notes OBJECTIVE: Correctly simplify polynomials expressions using addition, subtraction, and multiplication. Use the distributive property to multiply binomials, trinomials, and polynomials. Simplifying Expressions- Addition and Subtraction Identify and combine any like terms in the expression below. 3x − 2 + 14x − 3x 2 + 4 y − 1 + 2y 2 − 4 y − 21 y 2 + 4x 2 − 12 z + 7x 3x + 14 x + 7 x = 24 x −2 + −1 = −3 −3x 2 + 4 x 2 = 1x 2 4 y + −4 y = 0 2 y 2 + −21y 2 = −19 y 2 −12 z + −12 z A. 2 − 9 + 2x + 3x 2 − 5x + 10 − 1 3x 2 − 3x + 2 B. 2 x 3 + 2 x 2 + 4 x + 8 ( ) + 6 x 3 + 5 x 2 − 2 x − 7 ( ) 8 x 3 + 7 x 2 + 2 x + 1 C. x 2 + 3x − 7 ( ) − 3x 3 + 2 x 2 − 4 ( ) −3x 3 − x 2 + 3x − 3 D. 5 x 2 − 3x + 4 ( ) − 4 x 2 − 3x − 11 ( ) x 2 + 15 Addition Multiplication 3 + x = 3 + x 3 ⋅ x = 3x x + x = 2 x x ⋅ x = x 2 x + x + x = 3x x ⋅ x ⋅ x = x 3 − x + x = 0 − x ⋅ x = − x 2 2 x + 3x = 5 x 2 x ⋅ 3x = 6 x 2 7 x + x = 8 x 7 x ⋅ x = 7 x 2 4 x + 5 y = 4 x + 5 y 4 x ⋅ 5 y = 20 xy 2 x + x 2 = 2 x + x 2 2 x ⋅ x 2 = 2 x 3 x + x 2 + x 3 = x + x 2 + x 3 x ⋅ x 2 ⋅ x 3 = x 6 3x 2 + 5 y 4 = 3x 2 + 5 y 4 3x 2 ⋅ 5 y 4 = 15 x 2 y 4 3x 2 + 5 y 4