Question

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

Answer 1

Hello!

First, regroup the terms.
(3 - 2cd)(4 - 4 x 2cd)

Then, simplify 4 x 2cd to 8cd.
(3 - 2cd)(4 - 8cd)
That's your answer.

Enjoy.
~Isabella

Answer 2

 (3-c2d)(4-4c2d) Final result : -4 • (3 - c2d) • (c2d - 1)

Step by step solution :Step  1  :Equation at the end of step  1  : (3-((c2)•d))•(4-(22c2•d)) Step  2  :Step  3  :Pulling out like terms :

 3.1     Pull out like factors :

   4 - 4c2d  =   -4 • (c2d - 1) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  3 - c2d 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 = 
         A2 - B2

Note :  AB = BA is the commutative property of multiplication. 

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  3  is not a square !! 

Ruling : Binomial can not be factored as the
difference of two perfect squares

Trying to factor as a Difference of Squares :

 3.3      Factoring:  c2d - 1 

Check : 1 is the square of 1
Check :  c2  is the square of  c1 

Check :  d1   is not a square !! 
Ruling : Binomial can not be factored as the difference of two perfect squares

Final result : -4 • (3 - c2d) • (c2d - 1)