(a) To find the common factors of 25x^2y and 30xy^2, we first look at the numerical coefficients and the variables separately.

Numerical coefficients: The factors of 25 are 1, 5, and 25. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The common factors are 1 and 5.

Variables: The common factors are the variables that appear in both terms with the smallest exponent. Here, x appears in both terms, but with different exponents (2 in the first term and 1 in the second term). The smallest exponent is 1, so x^1 (or x) is a common factor. Similarly, y appears in both terms, but with different exponents (1 in the first term and 2 in the second term). The smallest exponent is 1, so y^1 (or y) is a common factor.

So, the common factors of 25x^2y and 30xy^2 are 5, x, and y.

(b) To find the common factors

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(a) To find the common factors of 25x^2y and 30xy^2, we first look at the numerical coefficients and the variables separately.

Numerical coefficients: The factors of 25 are 1, 5, and 25. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The common factors are 1 and 5.

Variables: The common factors are the variables that appear in both terms with the smallest exponent. Here, x appears in both terms, but with different exponents (2 in the first term and 1 in the second term). The smallest exponent is 1, so x^1 (or x) is a common factor. Similarly, y appears in both terms, but with different exponents (1 in the first term and 2 in the second term). The smallest exponent is 1, so y^1 (or y) is a common factor.

So, the common factors of 25x^2y and 30xy^2 are 5, x, and y.

(b) To find the common factors

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(a) To find the common factors of 25x^2y and 30xy^2, we first look at the numerical coefficients and the variables separately.

Numerical coefficients: The factors of 25 are 1, 5, and 25. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The common factors are 1 and 5.

Variables: The common factors are the variables that appear in both terms with the smallest exponent. Here, x appears in both terms, but with different exponents (2 in the first term and 1 in the second term). The smallest exponent is 1, so x^1 (or x) is a common factor. Similarly, y appears in both terms, but with different exponents (1 in the first term and 2 in the second term). The smallest exponent is 1, so y^1 (or y) is a common factor.

So, the common factors of 25x^2y and 30xy^2 are 5, x, and y.

(b) To find the common factors

What are the common factors of the following terms?(a) 25x2y, 30xy2(b) 63m3n, 54mn4

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