Final answer:
To factor out the GCF of the expression 63y^3x^2 + 7y^3x + 21y^5, identify the common factors of the terms and factor them out.
Step-by-step explanation:
To factor out the GCF (Greatest Common Factor) of the given expression, 63y^3x^2 + 7y^3x + 21y^5, we need to identify the common factors of all the terms.
The factors of 63 are 1, 3, 7, 9, 21, and 63.
The factors of y^3 are y^0, y^1, y^2, and y^3.
The factors of x^2 are x^0 and x^2.
Similarly, the factors of 7y^3x are 1, 3, 7, and y^3x.
And the factors of 21y^5 are 1, 3, 7, and y^5.
The GCF of the terms is 7y^3, so we can factor it out:
7y^3(9x^2 + x + 3y^2).