Question

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

Explanation:

Problem 13

Step1: Remove parentheses

$(6x^2 + 4x^3 + 1) - (x - 6x^3 - 4x^2) + (3 - 5x^3 - 8x + 3x^2)$
$=6x^2 + 4x^3 + 1 - x + 6x^3 + 4x^2 + 3 - 5x^3 - 8x + 3x^2$

Step2: Combine like terms (cubic terms)

$=(4x^3 + 6x^3 - 5x^3) + (6x^2 + 4x^2 + 3x^2) + (-x - 8x) + (1 + 3)$
$=5x^3 + 13x^2 - 9x + 4$

Step1: Remove parentheses

$(8x^3 + 2 - 7x^2) - (8x^3 + 4x^2 - 5x^4) + (x^3 + 2x^2 + 1 - 7x^4)$
$=8x^3 + 2 - 7x^2 - 8x^3 - 4x^2 + 5x^4 + x^3 + 2x^2 + 1 - 7x^4$

Step2: Combine like terms

$=(5x^4 - 7x^4) + (8x^3 - 8x^3 + x^3) + (-7x^2 - 4x^2 + 2x^2) + (2 + 1)$
$=-2x^4 + x^3 - 9x^2 + 3$

Step1: Remove parentheses

$(8x^2 - x + 3x^4) + (3x^4 + 4x^2 + 6) - (8x^2 - 5 + x^4 + 5x)$
$=8x^2 - x + 3x^4 + 3x^4 + 4x^2 + 6 - 8x^2 + 5 - x^4 - 5x$

Step2: Combine like terms

$=(3x^4 + 3x^4 - x^4) + (8x^2 + 4x^2 - 8x^2) + (-x - 5x) + (6 + 5)$
$=5x^4 + 4x^2 - 6x + 11$

Answer:

$5x^3 + 13x^2 - 9x + 4$

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Problem 14