Question

Factorise each of the following: x⁴ – 16y⁴​

Answer 1

Answer:(x + 2y)  •  (x - 2y)

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

Step-by-step explanation:

STEP  1  :  Equation at the end of step 1

              (x4) - 24y4

STEP  2  :  Trying to factor as a Difference of Squares:

2.1           Factoring:  x4-16y4  

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 :  x4  is the square of  x2  

Check :  y4  is the square of  y2  

Factorization is :       (x2 + 4y2)  •  (x2 - 4y2)  

Trying to factor as a Difference of Squares:

2.2      Factoring:  x2 - 4y2  

Check : 4 is the square of 2

Check :  x2  is the square of  x1  

Check :  y2  is the square of  y1  

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

Answer 2

Answer:

(X2+4y2)(x+2y)(x-2y)