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Answer:

The GCF of given expression is 4ab.

Step-by-step explanation:

The given expression is

[tex]12a^3b+8a^2b^2-20ab^3[/tex]

The factor form of each term is

[tex]12a^3b=2\times 2\times 3\times a\times a\times a\times b[/tex]

[tex]8a^2b=2\times 2\times 2\times a\times a\times b\times b[/tex]

[tex]-20ab^3=-2\times 2\times 5\times a\times b\times b\times b[/tex]

The common factors are 2,2,a,and b.

The GCF of given expression is

[tex]12a^3b=2\times 2\times a\times b=4ab[/tex]

Therefore the GCF of given expression is 4ab.

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The Greatest Common Factor of a given expression is 4ab.

What is the Greatest common factor?

In mathematics, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero.

The given expression is,

E = 12a³b + 8a²b² − 20ab³

To calculate the GCF factorize each term.

12a³b = 2 x 2 x 3 x a x a x a x a x b

8a²b²= 2 x 2 x 2 x a x a x b x b

−20ab³ = - 2 x 2 x 5 x a x b x b x b

The common factors are 2,2,a,and b.

The GCF of given expression is

12a³b + 8a²b² − 20ab³ = 4ab

Therefore, the GCF of given expression is 4ab.

To know more about the Greatest common factor follow

https://brainly.com/question/219464

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