Question

Can someone please answer this? I don't understand

Answer 1

Final result : (4x + 5y) • (16x2 - 20xy + 25y2)

Step by step solution :Step  1  :Equation at the end of step  1  : (64 • (x3)) + 53y3 Step  2  :Equation at the end of step  2  : 26x3 + 53y3 Step  3  :Trying to factor as a Sum of Cubes :

 3.1      Factoring:  64x3+125y3 

Theory : A sum of two perfect cubes,  a3 + b3can be factored into  :
             (a+b) • (a2-ab+b2)
Proof  : (a+b) • (a2-ab+b2) = 
    a3-a2b+ab2+ba2-b2a+b3 =
    a3+(a2b-ba2)+(ab2-b2a)+b3=
    a3+0+0+b3=
    a3+b3

Check :  64  is the cube of  4 

Check :  125  is the cube of   5 
Check :  x3 is the cube of   x1

Check :  y3 is the cube of   y1

Factorization is :
             (4x + 5y)  •  (16x2 - 20xy + 25y2) 

Trying to factor a multi variable polynomial :

 3.2    Factoring    16x2 - 20xy + 25y2 

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

 Factorization fails

Final result : (4x + 5y) • (16x2 - 20xy + 25y2)

Answer 2

answer is (4x)power3 + (√5y)power3 =( 4x+√5y){(4x)power2 + (√5y)power2 + 4√5xy}