factorization

Question

44⁴ - 66⁴

Answer 1

Hi Ushara,

 

To factorize this, it's useful to use the Difference of Squares factorization:

 

A² - B² = (A + B) * (A - B)

 

In your case, we have A = 44², and B = 66² (since (44²)² = 44⁴ and (66²)² = 66⁴:

 

44⁴-66⁴ = (44² + 66²) * (44² - 66²)

 

The first term, 44² + 66², can't be factorized (unless you do the prime factorizations suggested by Ebenezer, but I'm not sure that's what you're being asked to do).  The second term, however, is itself a difference of squares and can be factorized.  So since 44² - 66² = (44+66) * (44-66), you end up with:

 

44⁴-66⁴ = (44² + 66²) * (44 + 66) * (44 - 66)

 

Hope this helps!

Answer 2

44⁴ - 66⁴ ???

Using LCM (lowest common multiple), we'd have

 

(44)⁴ = ( 2 * 2* 11)⁴ = (2² * 11)⁴

 

for

 

(66)⁴  = ( 2 * 3* 11)⁴

 

that would then be;

 

(2² * 11)⁴ - ( 2 * 3* 11)⁴               ......................>>>>The Factors.

 

If you wanna go further and expand it

 

( 2⁸ * 11⁴) - ( 2⁴ *3⁴ *11⁴)

Answer 3

(44^4 - 66^4) =

 

(44^2 - 66 ^2) ( 44^2+ 66^2) =

 

( 44 - 66) ( 44 + 66) ( 44^2 + 66 ^2) =

 

( -22) ( 110) ( 44^2 + 66 ^2) =

 

- 242 ( 44^2 + 66 ^2 ) =

 

-242 ( 6292) =

 

  - 2 *11^2 ( 2^2 . 11^2 . 13)=

 

  - 2^3 . 11. ^4 . 13  / PRODUCTS OF ITS PRIME FACORS