Respuesta :

CastleRook
To get the GCF of the the expression, we look for the greatest factor of the expression:
42a5b3, 35a3b4, and 42ab4?
thus
(42a5b3, 35a3b4, 42ab4)
factoring b^3  which is the GCF of (b^3,b^4,b^4)we get:
b^3(42a^5,35a^3b,42ab)
next we factor our a which is the GCF of (a^5,a^3,a)
ab^3(42a^4,35a^2b, 42b^4)
next we factor out 7 which is the GCF of (42,35,42)
7ab^3(6a^4,5a^2b,6b^4)
hence the GCF is:
7ab^3

Answer:

[tex]7ab^3[/tex].

Step-by-step explanation:

We have been given three expressions. We are asked to find the greatest common factor of our expressions.

[tex]42a^4b^3[/tex], [tex]35a^3b^4[/tex], [tex]42ab^4[/tex]

The greatest common factor is the factor that divides two or more numbers.

Factors of coefficient:

42: 1, 2, 3, 6,7, 14, 21, 42

35: 1, 5, 7, 35

The greatest common factor of coefficient is 7.

Factors of [tex]a^5: a*a*a*a*a[/tex]

Factors of [tex]a^3: a*a*a[/tex]

Factors of [tex]a: 1*a[/tex]

The greatest common factor of [tex]a^5,a^3,a[/tex] is a.

Factors of [tex]b^3: b*b*b[/tex]

Factors of [tex]b^4: b*b*b*b[/tex]

The greatest common factor of [tex]b^3,b^4,b^4[/tex] is [tex]b^3[/tex].

Upon combining all these factors, we will get [tex]7ab^3[/tex].

Therefore, the greatest common factor of [tex]42a^4b^3[/tex], [tex]35a^3b^4[/tex] and [tex]42ab^4[/tex] is [tex]7ab^3[/tex].