Question

1. $-7 + 6k - 3k^4 - 5k + 1 + 8k^4 - k + 7$
2. $7n^3 + 7n^4 + 3 - 6n^4 + 2 - 2n^3 - 4 - 7n^3$
3. $-8a^4 - 7a - 7a^2 + 6a - 4a^2 + 8 - 1 - a^3$
4. $(-6 - 8x^4 + 3x) + (8x - 2x^4 - 3x^2) + (-3x^4 + 8 + 4x^2)$
5. $(-x^2 - 5 - 4x^4) + (3x^4 + 4 + 5x^2) + (-6x^4 + 8 - 3x^2)$
6. $(-4x^2 + 5x^3 + 3x^4) + (-x^2 + 1 - 3x^3) + (-4x^2 - 7 - 7x^3)$
7. $(3 - 6x^4 - 6x) + (7 - 7x + 2x^4) + (5 - 5x^4 + 8x)$

warm - up: simplify each expression.

1. $6n + 5n^3 - 6n + 7n^3$
2. $(7n^3 + 2n) + (-4n^3 + 6n + 5)$

Explanation:

Let's solve problem 15: \( 6n + 5n^3 - 6n + 7n^3 \)

Step 1: Combine like terms for \( n \)

The terms with \( n \) are \( 6n \) and \( -6n \).
\( 6n - 6n = 0 \)

Step 2: Combine like terms for \( n^3 \)

The terms with \( n^3 \) are \( 5n^3 \) and \( 7n^3 \).
\( 5n^3 + 7n^3 = 12n^3 \)

Answer:

\( 12n^3 \)