Final answer:
To factor the GCF out of 80y^6+70y^4, we find 10y^4 to be the GCF, resulting in a factored expression of 10y^4(8y^2 + 7).
Step-by-step explanation:
To factor the greatest common factor (GCF) out of the expression 80y6+70y4, we need to identify the largest number and the highest power of y that evenly divides into both terms. We see that the number 10 is the largest number that can divide into both 80 and 70 without a remainder. As for the variable y, the smallest exponent present in both terms is y4. Therefore, the GCF is 10y4.
After dividing both terms by the GCF, the expression becomes:
80y6+70y4 = 10y4(8y2 + 7)
Thus, the factored expression is 10y4(8y2 + 7).