Chapter 6: Q. 4 (page 572)

In the following exercises, find the greatest common factor.
$28 x^{2} y^{4}, 42 x^{4} y^{4}$

Short Answer

Expert verified

The GCF of the given expressions is $14 x^{2} y^{4}$ .

Step by step solution

Step 1. Given Information

The given expressions are $28 x^{2} y^{4}, 42 x^{4} y^{4}$ . $28 x^{2} y^{4}, 42 x^{4} y^{4}$

Step 2. Factoring

Factor each of the given expressions.

$28 x^{2} y^{4} = 2 \cdot 2 \cdot 7 \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y 42 x^{4} y^{4} = 2 \cdot 3 \cdot 7 \cdot x \cdot x \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y$

From the factors of the given expression, it is observed that the common factors are $2, 7, x, x, y, y, y, y$ .
Multiply the common factors to determine the GCF of the given expressions.

$2 \cdot 7 \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y = 14 x^{2} y^{4}$

So, the GCF of the given expressions is $14 x^{2} y^{4}$ .

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In the following exercises, find the greatest common factor.
$28 x^{2} y^{4}, 42 x^{4} y^{4}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Factoring

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Step by step solution

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In the following exercises, find the greatest common factor.
$28 x^{2} y^{4}, 42 x^{4} y^{4}$