Question

Factorise the polynomials 343 +125b3.​

Answer 1

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

343 + 53b3

STEP

2

:

Trying to factor as a Sum of Cubes:

2.1 Factoring: 125b3+343

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 : 343 is the cube of 7

Check : b3 is the cube of b1

Factorization is :

(5b + 7) • (25b2 - 35b + 49)