Simplify each sum \( (3 \) points each). 15) \( (2+n)+\left(5+6 n^{2}+2 n\right) \) Simplify each difference (3 points each) \( \left(2 p^{2}-2 p^{3}-5\right)+\left(2 p^{2}-2 p^{3}+3\right) \) 17) \( \left(7 p^{2}+6 p\right)-\left(3 p^{2}+2 p\right) \) Find each product \( (3 \) points each \( ) \) 19) \( (3 v-4)\left(4 v^{2}-2 v+1\right) \) \( 21)(x-1)(2 x-3)(x+3) \) 18) \( \left(x+7-7 x^{2}\right)-\left(3+x+x^{2}\right) \) 20) \( (6 n-7)\left(8 n^{2}+8 n-3\right) \)

To simplify the first expression, combine like terms: \((2 + n) + (5 + 6n^2 + 2n) = (2 + 5) + (n + 2n) + 6n^2 = 7 + 3n + 6n^2\). For the difference, you can add the two terms as they have the same structure: \((2p^2 - 2p^3 - 5) + (2p^2 - 2p^3 + 3) = (2p^2 + 2p^2) + (-2p^3 - 2p^3) + (-5 + 3) = 4p^2 - 4p^3 - 2\). Now for another difference, distribute and simplify: \((7p^2 + 6p) - (3p^2 + 2p) = (7p^2 - 3p^2) + (6p - 2p) = 4p^2 + 4p\). For the product: \((3v - 4)(4v^2 - 2v + 1)\) can be expanded using the distributive property: \(3v(4v^2) - 3v(2v) + 3v(1) - 4(4v^2) + 4(2v) - 4(1) = 12v^3 - 6v^2 + 3v - 16v^2 + 8v - 4 = 12v^3 - 22v^2 + 11v - 4\). Let's multiply the last product: \((6n - 7)(8n^2 + 8n - 3)\) gives: \(6n(8n^2) + 6n(8n) + 6n(-3) - 7(8n^2) - 7(8n) + 7(3) = 48n^3 + 48n^2 - 18n - 56n^2 - 56n + 21\), simplifying to \(48n^3 - 8n^2 - 74n + 21\).