Question

4.) (4n - 8)(2n - 3)
8n² - 28n + 24
6.) (1 + 4x - 3x² - x⁴) - (-6x⁴ + 5 - 6x)

Explanation:

Step1: Expand the first product via FOIL

$(4n-8)(2n-3) = 4n\cdot2n + 4n\cdot(-3) + (-8)\cdot2n + (-8)\cdot(-3)$
$=8n^2 -12n -16n +24$

Step2: Combine like terms for first problem

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

Step3: Distribute the negative sign

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

Step4: Combine like terms for second problem

$(-x^4+6x^4) -3x^2 + (4x+6x) + (1-5)$
$=5x^4 -3x^2 +10x -4$

Answer:

1. For $(4n-8)(2n-3)$: $8n^2 -28n +24$
2. For $(1 + 4x - 3x^2 - x^4) - (-6x^4 + 5 - 6x)$: $5x^4 - 3x^2 + 10x - 4$