Final answer:
The expression 18y¹⁸+42y¹¹-12y⁷ is factored by first finding the greatest common factor, which is 6y⁷, and then rewriting the expression as 6y⁷(3y¹¹ + 7y⁴ - 2).
Step-by-step explanation:
To factor the expression 18y¹⁸+42y¹¹-12y⁷ completely, we need to identify the greatest common factor among the terms. Looking at the coefficients 18, 42, and 12, we can see that 6 is a common factor. We can also factor out the smallest power of y which is y⁷. Therefore, we factor out 6y⁷ from each term.
First, divide each term by 6y⁷:
- 18y¹⁸ ÷ 6y⁷ = 3y¹¹
- 42y¹¹ ÷ 6y⁷ = 7y⁴
- -12y⁷ ÷ 6y⁷ = -2
Then, write the factored form:
6y⁷(3y¹¹ + 7y⁴ - 2)
The expression is now factored completely since the trinomial inside the parentheses cannot be factored further using integer coefficients.