Question

Multiply the polynomials.

Answer 1

Answer:

a. 12-16c²d+4c⁴d²

Step-by-step explanation:

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

• Open bracket using distributive property:

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

Answer 2

Answer:

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

Step-by-step 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