Question

${64x}^{3} - {125y}^{3}$
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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

$</p><p> {64x}^{3} - {125y}^{3} \\ </p><p>$

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 Difference of Cubes:

3.1 Factoring: 64x3-125y3

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 : 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)