What is the GCF of $18 a^{2} b^{2} - 6 a b^{2} + 12 a b^{3}$ $18a^2b^2 − 6ab^2 + 12ab^3$ ?

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What is the GCF of $18 a^{2} b^{2} - 6 a b^{2} + 12 a b^{3}$ $18a^2b^2 − 6ab^2 + 12ab^3$ ?

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Answer 1 · 2018-06-21T22:24:45

GCF is $6 a b^{2}$ $6ab^2$

Explanation:

Given: $18 a^{2} b^{2} - 6 a b^{2} + 12 a b^{3}$ $18a^2b^2 - 6ab^2 + 12 ab^3$

The GCF is the greatest common factor. TO find it you can decompose each monomial:

$18 a^{2} b^{2} : 2 \cdot 3 \cdot 3 \cdot a \cdot a \cdot b \cdot b$ $18a^2b^2: " "color(red)(2) * color(red)(3) * 3 * color(red)(a) * a * color(red)(b) * color(red)(b)$

$- 6 a b^{2} : - 1 \cdot 2 \cdot 3 \cdot a \cdot b \cdot b$ $-6ab^2: " "-1 * color(red)(2) * color(red)(3) * color(red)(a) * color(red)(b) *color(red)(b)$

$12 a b^{3} : 2 \cdot 2 \cdot 3 \cdot a \cdot b \cdot b \cdot b$ $12ab^3: " "color(red)(2) * 2 * color(red)(3) * color(red)(a) * color(red)(b) * color(red)(b) * b$

The GCF is $6 a b^{2}$ $6ab^2$

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What is the GCF of $18 a^{2} b^{2} - 6 a b^{2} + 12 a b^{3}$ $18a^2b^2 − 6ab^2 + 12ab^3$ ?

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Explanation:

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What is the GCF of $18 a^{2} b^{2} - 6 a b^{2} + 12 a b^{3}$ $18a^2b^2 − 6ab^2 + 12ab^3$ ?