-5y^3(y-6)+4y^3(y-7)
OK - first, distribute -5y^3 to the (y-6). You should get -5y^4+30y^3. Do the same thing by distributing 4y^3 to the (y-7), leaving you with 4y^4-28y^3. Then combine the y^4 terms and the y^3 terms to get the answer of -y^4+2y^3.
To distribute -5y^3 to (y-6), we multiply -5y^3 by each term in the parentheses:
-5y^3 * y = -5y^4
-5y^3 * -6 = +30y^3
Now, let's distribute 4y^3 to (y-7):
4y^3 * y = 4y^4
4y^3 * -7 = -28y^3
Now, we can combine like terms. The like terms in this equation are the terms with the same exponent, namely the y^4 terms and the y^3 terms:
(-5y^4 + 30y^3) + (4y^4 - 28y^3)
When we combine the y^4 terms, we have:
-5y^4 + 4y^4 = -y^4
When we combine the y^3 terms, we have:
30y^3 - 28y^3 = 2y^3
So the final answer is:
-y^4 + 2y^3