Question

Find the product: 2y^2(y^4-y^3-4y^2+4y+5)

Answer 1

Just multiply it out. So:

\[2y^2(y^4 - y^3 - 4y^2 + 4y + 5)\]
You have to distribute the \(2y^2\) throughout the parenthesized part:

\[2y^2 \cdot y^4 - 2y^2 \cdot y^3 - 2y^2 \cdot 4y^2 + 2y^2 \cdot 4y + 2y^2 \cdot 5\]
Can you go ahead and do those multiplications?

Answer 2

do i add or multiply the exponents?

Answer 3

When you multiply two different powers of the same number (or variable), you add the exponents. You would multiply them if you double raised. So:

\[3x^2 \cdot x^5 = 3x^{2 + 5} = 3x^7\]
\[(x^2)^5 = x^{2\cdot 5} = x^{10}\]

Answer 4

2y^2(y^4-y^3-4y^2+4y+5)

2y^6-2y^5-8y^6+8y^310y^2??

Answer 5

I think you messed up your third term. The rest look good.