Question

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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

TEP

1

:

Equation at the end of step 1

(125 • (a3)) - (23•33b3)

STEP

2

:

Equation at the end of step

2

:

53a3 - (23•33b3)

STEP

3

:

Trying to factor as a Difference of Cubes

3.1 Factoring: 125a3-216b3

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 : 125 is the cube of 5

Check : 216 is the cube of 6

Check : a3 is the cube of a1

Check : b3 is the cube of b1

Factorization is :

(5a - 6b) • (25a2 + 30ab + 36b2)

Trying to factor a multi variable polynomial :

3.2 Factoring 25a2 + 30ab + 36b2

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

Factorization fails

Final result :

(5a - 6b) • (25a2 + 30ab + 36b2