Question

125a^5b^2-27a^2b^5 factor​

Answer 1

Answer:

Step-by-step explanation:

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 : 27 is the cube of 3

Check : b3 is the cube of b1

Factorization is :

(5b + 3) • (25b2 - 15b + 9)

Answer 2

Step-by-step explanation:

Theory=>A sum of two perfect cubes ,a3 +b3 can be factorised 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 a cube of 5

27 is a cube of 3

b3 is a cube of b1

And the factorization is:-

(5b+3)•(25b2+15b+9)

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