directions: find each sum/difference. write all an
7. $(3a + 6) + (6a + 7)$
9. $(4x + 7) - (8 - 3x)$
11. $(x^2 + 7x - 6) + (x^2 + 6x + 3)$
13. $(4c^2 - 8c + 1) + (1 - 8c - 2c^2)$
15. $(7m^2 - 3 + m) - (2m + 3 + 10m^2)$
17. find the sum of $3 - a - 5a^2$ and $a - 7a^2 - 3$.
19. subtract $8v - 3v^3 + 6$ from $7 - 6v + 5v^3$.

Question

Accepted Answer

### Problem 7: $(3a + 6)+(6a + 7)$
# Explanation:
## Step1: Remove parentheses
$3a + 6+6a + 7$
## Step2: Combine like terms ($3a$ and $6a$; $6$ and $7$)
$(3a + 6a)+(6 + 7)=9a + 13$
# Answer: $9a + 13$

### Problem 9: $(4x + 7)-(8 - 3x)$
# Explanation:
## Step1: Distribute the negative sign
$4x + 7-8 + 3x$
## Step2: Combine like terms ($4x$ and $3x$; $7$ and $-8$)
$(4x + 3x)+(7 - 8)=7x-1$
# Answer: $7x - 1$

### Problem 11: $(x^{2}+7x - 6)+(x^{2}+6x + 3)$
# Explanation:
## Step1: Remove parentheses
$x^{2}+7x - 6+x^{2}+6x + 3$
## Step2: Combine like terms ($x^{2}$ and $x^{2}$; $7x$ and $6x$; $-6$ and $3$)
$(x^{2}+x^{2})+(7x + 6x)+(-6 + 3)=2x^{2}+13x - 3$
# Answer: $2x^{2}+13x - 3$

### Problem 13: $(4c^{2}-8c + 1)+(1 - 8c - 2c^{2})$
# Explanation:
## Step1: Remove parentheses
$4c^{2}-8c + 1+1 - 8c - 2c^{2}$
## Step2: Combine like terms ($4c^{2}$ and $-2c^{2}$; $-8c$ and $-8c$; $1$ and $1$)
$(4c^{2}-2c^{2})+(-8c-8c)+(1 + 1)=2c^{2}-16c + 2$
# Answer: $2c^{2}-16c + 2$

### Problem 15: $(7m^{2}-3 + m)-(2m + 3 + 10m^{2})$
# Explanation:
## Step1: Distribute the negative sign
$7m^{2}-3 + m-2m - 3-10m^{2}$
## Step2: Combine like terms ($7m^{2}$ and $-10m^{2}$; $m$ and $-2m$; $-3$ and $-3$)
$(7m^{2}-10m^{2})+(m - 2m)+(-3 - 3)=-3m^{2}-m - 6$
# Answer: $-3m^{2}-m - 6$

### Problem 17: Find the sum of $3 - a - 5a^{2}$ and $a - 7a^{2}-3$
# Explanation:
## Step1: Write the sum as an expression
$(3 - a - 5a^{2})+(a - 7a^{2}-3)$
## Step2: Remove parentheses
$3 - a - 5a^{2}+a - 7a^{2}-3$
## Step3: Combine like terms ($-5a^{2}$ and $-7a^{2}$; $-a$ and $a$; $3$ and $-3$)
$(-5a^{2}-7a^{2})+(-a + a)+(3 - 3)=-12a^{2}$
# Answer: $-12a^{2}$

### Problem 19: Subtract $8v-3v^{3}+6$ from $7 - 6v + 5v^{3}$
# Explanation:
## Step1: Write the subtraction as an expression
$(7 - 6v + 5v^{3})-(8v-3v^{3}+6)$
## Step2: Distribute the negative sign
$7 - 6v + 5v^{3}-8v + 3v^{3}-6$
## Step3: Combine like terms ($5v^{3}$ and $3v^{3}$; $-6v$ and $-8v$; $7$ and $-6$)
$(5v^{3}+3v^{3})+(-6v-8v)+(7 - 6)=8v^{3}-14v + 1$
# Answer: $8v^{3}-14v + 1$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 7: \((3a + 6)+(6a + 7)\)

Step1: Remove parentheses

Step2: Combine like terms (\(3a\) and \(6a\); \(6\) and \(7\))

Step1: Distribute the negative sign

Step2: Combine like terms (\(4x\) and \(3x\); \(7\) and \(-8\))

Step1: Remove parentheses

Step2: Combine like terms (\(x^{2}\) and \(x^{2}\); \(7x\) and \(6x\); \(-6\) and \(3\))

Answer:

Problem 9: \((4x + 7)-(8 - 3x)\)