Adding Polynomial Expressions

1. (-3x² +5x-19) + (4x²–2x)
   Answer: x²+3x-19

2. (3a²-4a) - (-2a² + 5²-9a+8)
   Answer: 5²-9a+8

3. (x²+x³+6) - (4x³-3x-1)
   Answer: 4x² + 3x³ +5

4. (2y² +3y+6) + (3y² +4y−1) - (2y²-4y-6)
   Answer: 3y²+37-1

5. (5x² +12x-4) - (2x² + x−3) + (3x² - 6x-4)
   Answer: 3x²+5x -5

6. (-a² +5a³+1) + (−4a³ − 2a +3) - (−a³ + 2a²+7)
   Answer: 4a³-3a²-2a-3

7. Subtract 2y² +5y+8 from 6y²-2y+3.
   Answer: 4y²-7y -5

8. From the sum of 2x²-3x-1 and +5x, subtract 5x²+2x+6.
   Answer: -3x³-5x - 1

9. Subtract 4x + 2x² +5 from the sum of 2x - 4x-3 and 3x4-3x² +9.
   Answer: -9x²-1

10. Write the polynomial which represents the perimeter of a triangle whose sides are represented by 2x²+3x, 5x²-1, and 3x² +7x-1.
    Answer: 30x²-30x-6

11. Represent the perimeter of a square whose side is 4x² + 3x-1.
    Answer: 16x² + 12x-4

12. Express the perimeter of a rectangular pasture whose length is 3x² - 2x+1 and whose width is x²-3x-6.
    Answer: 8x-10

Subtracting Polynomials

1. Subtract: (2a² + 5a + 3) − (a² − 3a - 4)
Answer: 3a² + 2a - 1

4. Subtract (2x² +9) from (3x-8)
Answer: 2x²-3x+1

5. Find the missing term: (2x + __ = 3x² + 3x-2
Answer: -5

10. A = -x³ + 2x² - 3
Answer: 3a²+8a+7

11. (x² + 7x + 1) − (3x² + ___ + 3) = 3x² - 2x - 8
Answer: 11x

9. A=7x³3x² - 6x + 2 and B = 2x³+4x²-5x-9. Find A - B.
Answer: 5x³ + 7x² - 11x + 7

13. A = x² - x + 1, B = 2x³ + 5x - 1, C = x² + 5. Find A + B - C.
Answer: x³ + 6x² - x - 5

Multiplying by a Monomial

1. Multiply: (8a³)(4a²)
Answer: 32a⁵

2. Multiply: (-3x²)³
Answer: -27x⁶

3. Multiply: (-5m²n)(-3m¹n²)
Answer: 15m³n²

4. Multiply: (3x²)(2x³)(-4x²)
Answer: -24x⁷

5. Multiply: (-5w²) [(² w³²) (²/¹)
Answer: -15w⁵

6. Multiply: -3b(3b³ +4b²)
Answer: -9b⁴ -12b³

7. Find: 3xy(2x² + y² − 2)
Answer: 6x³y + 3x²y² - 6xy

9. Simplify: 8a-2(4a - a)
Answer: 4a

Multiplying Binomials

1. Multiply: (a-1)(a + 4)
Answer: a² +3a-4

2. Which choice is equivalent to: (3x-2)(3x + 2)
Answer: (3x-2)²

3. Which choice is equivalent to: (2m-1)²
Answer: 4m² - 4m +1

4. Multiply: (3x+2y)(x+y)
Answer: 3x² +5xy+2y²

5. Multiply: (x-2)(x² + x + 1)
Answer: x³ + 3x² + 3x - 2

6. The base of a triangle is represented by (x + 4) and its height to that side is represented by (x-3). Express the area of the triangle.
Answer: x² +7x-12

Multiplying Polynomials

1. Multiply: (x-2)(x² + x + 1)
Answer: x³ + 3x² + 3x - 2

2. Multiply: x(x + 2y)(x + 3y)
Answer: x³ + 5x²y + 6y²