Question

Fully expand and simplify: ( 2 𝑦 + 5 ) ( 4 𝑦^4 + 7 𝑦 − 8 )

Answer 1

[AI-generated answer — Bot GPT 3.5]

To fully expand and simplify the given expression, we will use the distributive property:

(2y + 5)(4y^4 + 7y - 8)

First, distribute 2y to each term inside the second parentheses:
= 2y(4y^4) + 2y(7y) + 2y(-8)

= 8y^5 + 14y^2 - 16y

Next, distribute 5 to each term inside the second parentheses:
= 5(4y^4) + 5(7y) + 5(-8)

= 20y^4 + 35y - 40

Now, combine the results of both distributions:
= 8y^5 + 14y^2 - 16y + 20y^4 + 35y - 40

Simplify by combining like terms:
= 8y^5 + 20y^4 + 14y^2 - 16y + 35y - 40

Therefore, the fully expanded and simplified expression is:
8y^5 + 20y^4 + 14y^2 + 19y - 40