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Find the GCF of each pair of monomials:

1. [tex]\(8x^2y\)[/tex] and [tex]\(16xy\)[/tex]

2. [tex]\(8ab^3\)[/tex] and [tex]\(10a^2b^2\)[/tex]

Sagot :

GinnyAnsweridn
Sure, let's find the Greatest Common Factor (GCF) of each pair of monomials step-by-step.

### 1. Finding the GCF of [tex]\(8 x^2 y\)[/tex] and [tex]\(16 x y\)[/tex]:

1. Identify the numerical coefficients:
- The numerical coefficients are [tex]\(8\)[/tex] and [tex]\(16\)[/tex].

2. Find the GCF of the numerical coefficients:
- The GCF of [tex]\(8\)[/tex] and [tex]\(16\)[/tex] is [tex]\(8\)[/tex].

3. Identify the variable parts with their exponents:
- For [tex]\(8 x^2 y\)[/tex], we have [tex]\(x^2\)[/tex] and [tex]\(y^1\)[/tex].
- For [tex]\(16 x y\)[/tex], we have [tex]\(x^1\)[/tex] and [tex]\(y^1\)[/tex].

4. Find the GCF of the variable parts:
- For [tex]\(x\)[/tex]: The minimum exponent is [tex]\(1\)[/tex], so [tex]\(x^1 = x\)[/tex].
- For [tex]\(y\)[/tex]: The minimum exponent is [tex]\(1\)[/tex], so [tex]\(y^1 = y\)[/tex].

Combining the GCF of the numerical coefficients and the variable parts, the GCF of [tex]\(8 x^2 y\)[/tex] and [tex]\(16 x y\)[/tex] is:
[tex]\[8xy\][/tex]

### 2. Finding the GCF of [tex]\(8 a b^3\)[/tex] and [tex]\(10 a^2 b^2\)[/tex]:

1. Identify the numerical coefficients:
- The numerical coefficients are [tex]\(8\)[/tex] and [tex]\(10\)[/tex].

2. Find the GCF of the numerical coefficients:
- The GCF of [tex]\(8\)[/tex] and [tex]\(10\)[/tex] is [tex]\(2\)[/tex].

3. Identify the variable parts with their exponents:
- For [tex]\(8 a b^3\)[/tex], we have [tex]\(a^1\)[/tex] and [tex]\(b^3\)[/tex].
- For [tex]\(10 a^2 b^2\)[/tex], we have [tex]\(a^2\)[/tex] and [tex]\(b^2\)[/tex].

4. Find the GCF of the variable parts:
- For [tex]\(a\)[/tex]: The minimum exponent is [tex]\(1\)[/tex], so [tex]\(a^1 = a\)[/tex].
- For [tex]\(b\)[/tex]: The minimum exponent is [tex]\(2\)[/tex], so [tex]\(b^2 = b^2\)[/tex].

Combining the GCF of the numerical coefficients and the variable parts, the GCF of [tex]\(8 a b^3\)[/tex] and [tex]\(10 a^2 b^2\)[/tex] is:
[tex]\[2ab^2\][/tex]

So, the GCFs are:
1. [tex]\(8xy\)[/tex]
2. [tex]\(2ab^2\)[/tex]
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