Question

Multiply the polynomials.

(3-c²d)(4-4c²d)

a. 12-16c²d+4c⁴d²
b. 12+4c⁴d²
c. 7-3c⁴a²
d. 7-5c²d-3c⁴a²​

Answer 1

4c^4d^2 - 16dc^2 + 12

Explanation:

(3 - 1c^2d)(4 - 4c^2d)

First, you rearrange the terms:

(-c^2d + 3)(4 - 4c^2d)

(-c^2d + 3)(-4c^2d + 4)

Distribute:

(-4c^2d + 4)(-c^2d) + 3 (-4c^2 + 4)

We want the constants to be on the left, in order to do that, you re-order the terms:

-(-4c^2d + 4)c^2 + 3(-4c^2d + 4)

Distribute:

-(-4c^4d^2 + 4dc^2) + 3 (-4c^2d + 4)

4c^4d^2 + 3 (-4c^2d + 4)

4c^4d^2 - 16dc^2 + 12

Answer 2

a. 12-16c²d+4c⁴d²

Explanation:

`{ \tt{(3 - {c}^(2) d)(4 - 4 {c}^(2) d)}}`

• Open bracket using distributive property:

`= { \tt{(3 * 4) + (3 * - 4 {c}^(2)d) + ( - {c}^(2)d * 4) + ( - {c}^(2) d * - 4 {c}^(2) d) }} \\ = { \tt{12 - 12 {c}^(2) d - 4 {c}^(2) d + 4 {c}^(4) {d}^(2) }} \\ { \tt{ = {4c}^(4) {d}^(2) - 16 {c}^(2)d + 12 }}`