Question

3. Factorisation of 8x^3 - 2xy^2 is​

Answer 1

STEP1:Equation at the end of step 1

(8 • (x3)) - 2xy2

STEP 2 :

Equation at the end of step2:

23x3 - 2xy2

STEP3:

STEP4:Pulling out like terms

 4.1     Pull out like factors :

   8x3 - 2xy2  =   2x • (4x2 - y2) 

Trying to factor as a Difference of Squares:

 4.2      Factoring:  4x2 - y2 

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 :  x2  is the square of  x1 

Check :  y2  is the square of  y1 

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

Final result :

2x • (2x + y) • (2x - y)