Question

3.) $(-8 + a^{2} - 3a^{4}) + (-4a^{2} - 4a - 2a^{4})$ $-8 + -3^{(2 + 4)}$ $16a^{6}$ $-2a^{2} -$ 4.) $(4n - 8)(2n - 3)$ 5.) $\frac{-6k^{4} + 15k^{3} - 9k^{2}}{3k^{2}}$ 6.) $(1 + 4x - 3x^{2} - x^{4}) - (-6x^{4} + 5 -$

Explanation:

Step1: Combine like terms (Problem 3)

$(-8 + a^2 - 3a^4) + (-4a^2 - 4a - 2a^4) = -8 -4a + (a^2-4a^2) + (-3a^4-2a^4)$

Step2: Simplify each term group

$=-8 -4a -3a^2 -5a^4$

Step3: Apply FOIL method (Problem4)

$(4n-8)(2n-3) = 4n\cdot2n + 4n\cdot(-3) -8\cdot2n -8\cdot(-3)$

Step4: Calculate and combine terms

$=8n^2 -12n -16n +24 = 8n^2 -28n +24$

Step5: Split fraction (Problem5)

$\frac{-6k^4 +15k^3 -9k^2}{3k^2} = \frac{-6k^4}{3k^2} + \frac{15k^3}{3k^2} - \frac{9k^2}{3k^2}$

Step6: Simplify each fraction

$=-2k^2 +5k -3$

Answer:

3.) $-5a^4 -3a^2 -4a -8$
4.) $8n^2 -28n +24$
5.) $-2k^2 +5k -3$
6.) (The problem is incomplete; cannot solve without full second polynomial)