fully expand and simplfy

Question

(5y^3+2)(4y^7+8y−3)

Answer 1

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