5.2 adding and subtracting polynomials practice
simplify each expression. write all answers in descending order.
1. $(b - 10) + (4b - 3)$
2. $(p^2 + p + 3) - (-4p^2 - p + 3)$
3. $(-4m^2 - 6m) - (6m + 4m^2)$
4. $(m^2 - m - 2) + (-m + 7m^2)$
5. $(-k + 5) - (3k^2 - 6)$
6. $(18p^2 + 11p - q^2) - (15p^2 - 3pq + 4q^2)$
7. $(12xy - 8x + 3y) + (15x - 7y - 8xy)$
8. $(3bc - 9b^2 - 6c^2) + (4c^2 - b^2 + 5bc)$
9. $(3x^2 + 12x - 7) - (5x^2 - 19)$
10. $(5x^2 - 19) - (3x^2 + 12x - 7)$

Question

Accepted Answer

### Problem 1: $(b - 10)+(4b - 3)$
# Explanation:
## Step 1: Remove parentheses
Since there are no negative signs outside the parentheses, we can directly remove them: $b - 10+4b - 3$
## Step 2: Combine like terms
Combine the $b$ terms: $b + 4b=5b$
Combine the constant terms: $-10-3 = -13$
# Answer: $5b-13$

### Problem 2: $(p^{2}+p + 3)-(-4p^{2}-p + 3)$
# Explanation:
## Step 1: Distribute the negative sign
Multiply each term inside the second parentheses by $-1$: $p^{2}+p + 3 + 4p^{2}+p - 3$
## Step 2: Combine like terms
For $p^{2}$ terms: $p^{2}+4p^{2}=5p^{2}$
For $p$ terms: $p + p = 2p$
For constant terms: $3-3=0$
# Answer: $5p^{2}+2p$

### Problem 3: $(-4m^{2}-6m)-(6m + 4m^{2})$
# Explanation:
## Step 1: Distribute the negative sign
$-4m^{2}-6m-6m - 4m^{2}$
## Step 2: Combine like terms
For $m^{2}$ terms: $-4m^{2}-4m^{2}=-8m^{2}$
For $m$ terms: $-6m-6m=-12m$
# Answer: $-8m^{2}-12m$

### Problem 4: $(m^{2}-m - 2)+(-m + 7m^{2})$
# Explanation:
## Step 1: Remove parentheses
$m^{2}-m - 2 - m + 7m^{2}$
## Step 2: Combine like terms
For $m^{2}$ terms: $m^{2}+7m^{2}=8m^{2}$
For $m$ terms: $-m - m=-2m$
For constant terms: $-2$ (no other constant terms to combine with)
# Answer: $8m^{2}-2m - 2$

### Problem 5: $(-k + 5)-(3k^{2}-6)$
# Explanation:
## Step 1: Distribute the negative sign
$-k + 5-3k^{2}+6$
## Step 2: Combine like terms
Rearrange in descending order: $-3k^{2}-k+(5 + 6)$
Combine constant terms: $5 + 6 = 11$
# Answer: $-3k^{2}-k + 11$

### Problem 6: $(18p^{2}+11p - q^{2})-(15p^{2}-3pq + 4q^{2})$
# Explanation:
## Step 1: Distribute the negative sign
$18p^{2}+11p - q^{2}-15p^{2}+3pq - 4q^{2}$
## Step 2: Combine like terms
For $p^{2}$ terms: $18p^{2}-15p^{2}=3p^{2}$
For $q^{2}$ terms: $-q^{2}-4q^{2}=-5q^{2}$
For $p$ term: $11p$ (no other $p$ terms to combine with)
For $pq$ term: $3pq$ (no other $pq$ terms to combine with)
# Answer: $3p^{2}+11p + 3pq-5q^{2}$

### Problem 7: $(12xy-8x + 3y)+(15x - 7y-8xy)$
# Explanation:
## Step 1: Remove parentheses
$12xy-8x + 3y+15x - 7y-8xy$
## Step 2: Combine like terms
For $xy$ terms: $12xy-8xy = 4xy$
For $x$ terms: $-8x + 15x=7x$
For $y$ terms: $3y-7y=-4y$
# Answer: $4xy + 7x-4y$

### Problem 8: $(3bc-9b^{2}-6c^{2})+(4c^{2}-b^{2}+5bc)$
# Explanation:
## Step 1: Remove parentheses
$3bc-9b^{2}-6c^{2}+4c^{2}-b^{2}+5bc$
## Step 2: Combine like terms
For $b^{2}$ terms: $-9b^{2}-b^{2}=-10b^{2}$
For $c^{2}$ terms: $-6c^{2}+4c^{2}=-2c^{2}$
For $bc$ terms: $3bc + 5bc=8bc$
# Answer: $-10b^{2}+8bc-2c^{2}$

### Problem 9: $(3x^{2}+12x - 7)-(5x^{2}-19)$
# Explanation:
## Step 1: Distribute the negative sign
$3x^{2}+12x - 7-5x^{2}+19$
## Step 2: Combine like terms
For $x^{2}$ terms: $3x^{2}-5x^{2}=-2x^{2}$
For $x$ term: $12x$ (no other $x$ terms to combine with)
For constant terms: $-7 + 19 = 12$
# Answer: $-2x^{2}+12x + 12$

### Problem 10: $(5x^{2}-19)-(3x^{2}+12x - 7)$
# Explanation:
## Step 1: Distribute the negative sign
$5x^{2}-19-3x^{2}-12x + 7$
## Step 2: Combine like terms
For $x^{2}$ terms: $5x^{2}-3x^{2}=2x^{2}$
For $x$ term: $-12x$ (no other $x$ terms to combine with)
For constant terms: $-19 + 7=-12$
# Answer: $2x^{2}-12x - 12$

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QUESTION IMAGE

Question

Explanation:

Problem 1: \((b - 10)+(4b - 3)\)

Step 1: Remove parentheses

Step 2: Combine like terms

Step 1: Distribute the negative sign

Step 2: Combine like terms

Step 1: Distribute the negative sign

Step 2: Combine like terms

Answer:

Problem 2: \((p^{2}+p + 3)-(-4p^{2}-p + 3)\)