Question

Multiplying polynomials

Solve the following.

1. (x + 8) (x + b)



2. (3x – 2) (x – 2)



3.

(2x + 1) (x – 1)



4.

(a - b) (a2 + ab + b^2)



5. (5x + 2) (6x^3 x 2y - 1)

Answer 1

Answer:

1) x^2 + (b+8)x + 8b

2) 3x^2 - 8x + 4

3) 2x^2 - x - 1

4) a^3 - b^3

5) 30x^4 y - 10x + 12x^3 y - 4xy

Step-by-step explanation: The answer to (x + 8) (x + b) is x^2 + (b+8)x + 8b, which is found using the FOIL method.

The answer to (3x – 2) (x – 2) is 3x^2 - 8x + 4, which is also found using the FOIL method.

The answer to (2x + 1) (x – 1) is 2x^2 - x - 1, which is also found using the FOIL method.

The answer to (a - b) (a^2 + ab + b^2) is a^3 - b^3, which is found using the formula for the difference of cubes.

The answer to (5x + 2) (6x^3 x 2y - 1) is 30x^4 y - 10x + 12x^3 y - 4xy, which is found using the FOIL method.

Answer 2

1. (x + 8)(x + b) = x² + bx + 8x + 8b = x² + (b + 8)x + 8b

2. (3x - 2)(x - 2) = 3x² - 6x - 2x + 4 = 3x² - 8x + 4

3. (2x + 1)(x - 1) = 2x² - 2x + x - 1 = 2x² - x - 1

4. (a - b)(a² + ab + b²) = a³ - b³

5. (5x + 2)(6x³x²y - 1) = 30x^4 x²y + 12x³x²y - 5x - 2

Explanation: