Question

algebra 2
name
id: 1
unit 3 quiz 1 practice
date
period
simplify.

1. $\begin{bmatrix} -1 & -6 \\ 4 & -6 end{bmatrix}+\begin{bmatrix} -3 & -2 \\ 1 & -4 end{bmatrix}$
2. $\begin{bmatrix} 4 \\ -6 end{bmatrix}-\begin{bmatrix} 1 \\ 2 end{bmatrix}$
3. $-4\begin{bmatrix} -2 & 5 \\ 2 & 0 \\ 5 & 3 end{bmatrix}$
4. $\begin{bmatrix} 2 & -2 \\ -5 & 6 end{bmatrix}-\begin{bmatrix} -5 & 4 \\ 2 & -2 end{bmatrix}$
5. $\begin{bmatrix} -2 \\ -5 end{bmatrix}+\begin{bmatrix} -1 \\ 1 end{bmatrix}$
6. $-3\begin{bmatrix} -5 & -5 \\ 0 & 3 end{bmatrix}$

simplify each expression.

1. $\frac{b - 3}{b^{2}+5b - 24}$
2. $\frac{3x + 18}{x + 6}$
3. $\frac{x - 10}{x^{2}-5x - 50}$
4. $\frac{4k^{2}-32k}{k - 8}$
5. $\frac{m^{2}-2m - 48}{m^{2}+9m + 18}$
6. $\frac{x^{2}+7x + 6}{9x + 54}$
7. $\frac{x + 7}{x^{2}+10x + 21}div\frac{1}{10x}$
8. $\frac{9b + 27}{b + 3}cdot\frac{1}{8b^{2}}$
9. $\frac{5k + 35}{k - 5}cdot\frac{k - 5}{5}$
10. $\frac{v - 4}{v - 2}div\frac{v + 8}{v^{2}+6v - 16}$
11. $\frac{2}{k + 3}div\frac{k + 2}{k^{2}+5k + 6}$
12. $\frac{6}{n + 7}cdot\frac{n^{2}+6n - 7}{n - 1}$

Explanation:

1) Step1: Add corresponding elements

$$\begin{bmatrix}-1+(-3) & -6+(-2) \\ 4+1 & -6+(-4)\end{bmatrix} = \begin{bmatrix}-4 & -8 \\ 5 & -10\end{bmatrix}$$

2) Step1: Subtract corresponding elements

$$\begin{bmatrix}4-1 \\ -6-2\end{bmatrix} = \begin{bmatrix}3 \\ -8\end{bmatrix}$$

3) Step1: Multiply by scalar -4

$$\begin{bmatrix}-4\times(-2) & -4\times5 \\ -4\times2 & -4\times0 \\ -4\times5 & -4\times3\end{bmatrix} = \begin{bmatrix}8 & -20 \\ -8 & 0 \\ -20 & -12\end{bmatrix}$$

4) Step1: Subtract corresponding elements

$$\begin{bmatrix}2-(-5) & -2-4 \\ -5-2 & 6-(-2)\end{bmatrix} = \begin{bmatrix}7 & -6 \\ -7 & 8\end{bmatrix}$$

5) Step1: Add corresponding elements

$$\begin{bmatrix}-2+(-1) \\ -5+1\end{bmatrix} = \begin{bmatrix}-3 \\ -4\end{bmatrix}$$

6) Step1: Multiply by scalar -3

$$\begin{bmatrix}-3\times(-5) & -3\times(-5) \\ -3\times0 & -3\times3\end{bmatrix} = \begin{bmatrix}15 & 15 \\ 0 & -9\end{bmatrix}$$

7) Step1: Factor denominator

$b^2+5b-24=(b+8)(b-3)$

Step2: Cancel common factors

$\frac{b-3}{(b+8)(b-3)} = \frac{1}{b+8}$

8) Step1: Factor numerator

$3x+18=3(x+6)$

Step2: Cancel common factors

$\frac{3(x+6)}{x+6}=3$

9) Step1: Factor denominator

$x^2-5x-50=(x+5)(x-10)$

Step2: Cancel common factors

$\frac{x-10}{(x+5)(x-10)}=\frac{1}{x+5}$

10) Step1: Factor numerator

$4k^2-32k=4k(k-8)$

Step2: Cancel common factors

$\frac{4k(k-8)}{k-8}=4k$

11) Step1: Factor numerator and denominator

$m^2-2m-48=(m-8)(m+6)$, $m^2+9m+18=(m+3)(m+6)$

Step2: Cancel common factors

$\frac{(m-8)(m+6)}{(m+3)(m+6)}=\frac{m-8}{m+3}$

12) Step1: Factor numerator and denominator

$x^2+7x+6=(x+1)(x+6)$, $9x+54=9(x+6)$

Step2: Cancel common factors

$\frac{(x+1)(x+6)}{9(x+6)}=\frac{x+1}{9}$

13) Step1: Factor denominator

$x^2+10x+21=(x+3)(x+7)$

Step2: Rewrite division as multiplication

$\frac{x+7}{(x+3)(x+7)} \times 10x$

Step3: Cancel common factors

$\frac{10x}{x+3}$

14) Step1: Factor numerator

$9b+27=9(b+3)$

Step2: Cancel common factors

$\frac{9(b+3)}{b+3} \times \frac{1}{8b^2} = \frac{9}{8b^2}$

15) Step1: Factor numerator

$5k+35=5(k+7)$

Step2: Cancel common factors

$\frac{5(k+7)}{k-5} \times \frac{k-5}{5} = k+7$

16) Step1: Factor denominator

$v^2+6v-16=(v+8)(v-2)$

Step2: Rewrite division as multiplication

$\frac{v-4}{v-2} \times \frac{(v+8)(v-2)}{v+8}$

Step3: Cancel common factors

$v-4$

17) Step1: Factor denominator

$k^2+5k+6=(k+2)(k+3)$

Step2: Rewrite division as multiplication

$\frac{2}{k+3} \times \frac{(k+2)(k+3)}{k+2}$

Step3: Cancel common factors

$2(k+2)$

18) Step1: Factor numerator

$n^2+6n-7=(n+7)(n-1)$

Step2: Cancel common factors

$\frac{6}{n+7} \times \frac{(n+7)(n-1)}{n-1} = 6(n-1)$

Answer:

1)

$$\begin{bmatrix}-4 & -8 \\ 5 & -10\end{bmatrix}$$

2)

$$\begin{bmatrix}3 \\ -8\end{bmatrix}$$

3)

$$\begin{bmatrix}8 & -20 \\ -8 & 0 \\ -20 & -12\end{bmatrix}$$

4)

$$\begin{bmatrix}7 & -6 \\ -7 & 8\end{bmatrix}$$

5)

$$\begin{bmatrix}-3 \\ -4\end{bmatrix}$$

6)

$$\begin{bmatrix}15 & 15 \\ 0 & -9\end{bmatrix}$$

1. $\frac{1}{b+8}$
2. $3$
3. $\frac{1}{x+5}$
4. $4k$
5. $\frac{m-8}{m+3}$
6. $\frac{x+1}{9}$
7. $\frac{10x}{x+3}$
8. $\frac{9}{8b^2}$
9. $k+7$
10. $v-4$
11. $2(k+2)$
12. $6(n-1)$