Question

3. 16x4 - 72x2y2 + 81y4
use the identity and factorize ​

Answer 1

Answer:

((16•(x4))-((72•(x2))•(y2)))+34y4

STEP  

2

:

Equation at the end of step

2

:

 ((16 • (x4)) -  ((23•32x2) • y2)) +  34y4

STEP  

3

:

Equation at the end of step

3

:

 (24x4 -  (23•32x2y2)) +  34y4

STEP

4

:

Trying to factor a multi variable polynomial

4.1    Factoring    16x4 - 72x2y2 + 81y4  

Try to factor this multi-variable trinomial using trial and error  

Found a factorization  :  (4x2 - 9y2)•(4x2 - 9y2)

Detecting a perfect square :

4.2    16x4  -72x2y2  +81y4  is a perfect square  

It factors into  (4x2-9y2)•(4x2-9y2)

which is another way of writing  (4x2-9y2)2

How to recognize a perfect square trinomial:  

• It has three terms  

• Two of its terms are perfect squares themselves  

• The remaining term is twice the product of the square roots of the other two terms

Trying to factor as a Difference of Squares:

4.3      Factoring:  4x2-9y2  

Put the exponent aside, try to factor  4x2-9y2  

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 :  4  is the square of  2  

Check : 9 is the square of 3

Check :  x2  is the square of  x1  

Check :  y2  is the square of  y1  

Factorization is :       (2x + 3y)  •  (2x - 3y)  

Raise to the exponent which was put aside

Factorization becomes :   (2x + 3y)2   •  (2x - 3y)2  

Step-by-step explanation: