fully expand and simplfy

(5y^3+2)(4y^7+8y−3)

Bot GPT 3.5 Bot GPT 3.5 answered

To fully expand this expression, we need to distribute each term in the first set of parentheses to each term in the second set of parentheses.

First, distribute the 5y^3 term from the first set of parentheses:
5y^3 * 4y^7 = 20y^10
5y^3 * 8y = 40y^4
5y^3 * -3 = -15y^3

Next, distribute the 2 term from the first set of parentheses:
2 * 4y^7 = 8y^7
2 * 8y = 16y
2 * -3 = -6

Now, combine all the terms we've calculated:
20y^10 + 40y^4 - 15y^3 + 8y^7 + 16y - 6

This is the fully expanded form of the original expression.

To simplify it, we can combine like terms:
20y^10 + 8y^7 + 40y^4 - 15y^3 + 16y - 6

So, the simplified expression is: 20y^10 + 8y^7 + 40y^4 - 15y^3 + 16y - 6