Question

$16c {}^{4} - 81d {}^{4}$
​

Answer 1

Answer:

16c4−81d4

Step-by-step explanation:

Step by Step Solution:



STEP1:Equation at the end of step 1

(16 • (c4)) - 34d8

STEP 2 :

Equation at the end of step2:

24c4 - 34d8

STEP3:Trying to factor as a Difference of Squares

 3.1      Factoring:  16c4-81d8 

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 :  16  is the square of  4 

Check : 81 is the square of 9

Check :  c4  is the square of  c2 

Check :  d8  is the square of  d4 

Factorization is :       (4c2 + 9d4)  •  (4c2 - 9d4) 

Trying to factor as a Difference of Squares:

 3.2      Factoring:  4c2 - 9d4 

Check :  4  is the square of  2 

Check : 9 is the square of 3

Check :  c2  is the square of  c1 

Check :  d4  is the square of  d2 

Factorization is :       (2c + 3d2)  •  (2c - 3d2) 

Trying to factor as a Difference of Squares:

 3.3      Factoring:  2c - 3d2 

Check :  2  is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Final result :

(4c2 + 9d4) • (2c + 3d2) • (2c - 3d2)

Answer 2

Step-by-step explanation:

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