Question

warm-up quiz
qtr-3, #1
1.) $(-8 + a^2 - 3a^3) + (-4a^3 + 4a - 2a^2)$
2.)
3.) $(4n - 8)(2n - 3)$
$()()$
4.) $(2x + 7)^2$
5.) $\frac{2n^3 + 8n^2 - 20n}{2n} = $

Explanation:

Step1: Combine like terms (Problem 1)

$(-8 + a^2 - 3a^3) + (-4a^3 + 4a - 2a^2) = -8 + 4a + (a^2 - 2a^2) + (-3a^3 - 4a^3)$
$= -8 + 4a - a^2 -7a^3$

Step2: Expand via distributive property (Problem 3)

$(4n - 8)(2n - 3) = 4n(2n) + 4n(-3) -8(2n) -8(-3)$
$=8n^2 -12n -16n +24$
$=8n^2 -28n +24$

Step3: Expand squared binomial (Problem 4)

$(2x+7)^2 = (2x)^2 + 2(2x)(7) +7^2$
$=4x^2 +28x +49$

Step4: Divide each term (Problem 5)

$\frac{2n^3 +8n^2 -20n}{2n} = \frac{2n^3}{2n} + \frac{8n^2}{2n} - \frac{20n}{2n}$
$=n^2 +4n -10$

Answer:

1. $-7a^3 -a^2 +4a -8$
2. $8n^2 -28n +24$
3. $4x^2 +28x +49$
4. $n^2 +4n -10$

Note: Problem 2 is not fully legible and cannot be solved accurately; please provide the complete, clear problem for assistance.