Question

12. What are the factors of 32x
4 - 500x?​

Answer 1

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

25x4 - 500x

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

32x4 - 500x = 4x • (8x3 - 125)

Trying to factor as a Difference of Cubes:

3.2 Factoring: 8x3 - 125

Theory : A difference of two perfect cubes, a3 - b3 can 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 : 8 is the cube of 2

Check : 125 is the cube of 5

Check : x3 is the cube of x1

Factorization is :

(2x - 5) • (4x2 + 10x + 25)

Answer 2

Step-by-step explanation:

32x 4 -500x

=2×2×2×2×2×2×2-5×5×5×4

_____________________

=32=2×2×2×2×2

=4=2×2

=500=5×5×5×4

Hope it will help you

Have a nice Day