Question

Factorize x^3-125y^3​

Answer 1

Answer:

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(x3) + 53y3

Step 2 :

Trying to factor as a Sum of Cubes :

2.1 Factoring: x3+125y3

Theory : A sum 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 : 125 is the cube of 5

Check : x3 is the cube of x1

Check : y3 is the cube of y1

Factorization is :

(x + 5y) • (x2 - 5xy + 25y2)

final answer is :

(x + 5y) • (x2 - 5xy + 25y2)

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