adv alg
alg review quiz
simplify each sum.
1) ((7x^4 - x^3 - 6x)+(6x^4 - 8x + 4x^3)) 2) ((7x^2 - 7x + 3x^3)+(6x^3 - 3x + 2x^2))

simplify each difference.
3) ((8n^3 + 6n^2 - 3n)-(5n^3 - 2n - 2n^2)) 4) ((2x^2 - 4x^4 - 5)-(8x^4 + x^2 - 3))

find each product.
5) ((2x + 3)(x - 8)) 6) ((3n + 7)(6n + 2))
7) ((8n - 1)(4n + 2))

factor each completely.
8) (k^2 + 9k + 20) 9) (v^2 + 10v + 9)

Question

adv alg
alg review quiz
simplify each sum.
1) ((7x^4 - x^3 - 6x)+(6x^4 - 8x + 4x^3))  2) ((7x^2 - 7x + 3x^3)+(6x^3 - 3x + 2x^2))

simplify each difference.
3) ((8n^3 + 6n^2 - 3n)-(5n^3 - 2n - 2n^2))  4) ((2x^2 - 4x^4 - 5)-(8x^4 + x^2 - 3))

find each product.
5) ((2x + 3)(x - 8))  6) ((3n + 7)(6n + 2))
7) ((8n - 1)(4n + 2))

factor each completely.
8) (k^2 + 9k + 20)  9) (v^2 + 10v + 9)

Accepted Answer

### Problem 1: Simplify $(7x^4 - x^3 - 6x) + (6x^4 - 8x + 4x^3)$
# Explanation:
## Step 1: Combine like terms for $x^4$
$7x^4 + 6x^4 = 13x^4$
## Step 2: Combine like terms for $x^3$
$-x^3 + 4x^3 = 3x^3$
## Step 3: Combine like terms for $x$
$-6x - 8x = -14x$
# Answer:
$13x^4 + 3x^3 - 14x$

### Problem 2: Simplify $(7x^2 - 7x + 3x^3) + (6x^3 - 3x + 2x^2)$
# Explanation:
## Step 1: Combine like terms for $x^3$
$3x^3 + 6x^3 = 9x^3$
## Step 2: Combine like terms for $x^2$
$7x^2 + 2x^2 = 9x^2$
## Step 3: Combine like terms for $x$
$-7x - 3x = -10x$
# Answer:
$9x^3 + 9x^2 - 10x$

### Problem 3: Simplify $(8n^2 + 6n^3 - 3n) - (5n^3 - 2n - 2n^2)$
# Explanation:
## Step 1: Distribute the negative sign
$8n^2 + 6n^3 - 3n - 5n^3 + 2n + 2n^2$
## Step 2: Combine like terms for $n^3$
$6n^3 - 5n^3 = n^3$
## Step 3: Combine like terms for $n^2$
$8n^2 + 2n^2 = 10n^2$
## Step 4: Combine like terms for $n$
$-3n + 2n = -n$
# Answer:
$n^3 + 10n^2 - n$

### Problem 4: Simplify $(2x^2 - 4x^4 - 5) - (8x^4 + x^2 - 3)$
# Explanation:
## Step 1: Distribute the negative sign
$2x^2 - 4x^4 - 5 - 8x^4 - x^2 + 3$
## Step 2: Combine like terms for $x^4$
$-4x^4 - 8x^4 = -12x^4$
## Step 3: Combine like terms for $x^2$
$2x^2 - x^2 = x^2$
## Step 4: Combine constant terms
$-5 + 3 = -2$
# Answer:
$-12x^4 + x^2 - 2$

### Problem 5: Find the product $(2x + 3)(x - 8)$
# Explanation:
## Step 1: Use the distributive property (FOIL method)
$2x \cdot x + 2x \cdot (-8) + 3 \cdot x + 3 \cdot (-8)$
## Step 2: Simplify each term
$2x^2 - 16x + 3x - 24$
## Step 3: Combine like terms
$-16x + 3x = -13x$
# Answer:
$2x^2 - 13x - 24$

### Problem 6: Find the product $(3n + 7)(6n + 2)$
# Explanation:
## Step 1: Use the distributive property (FOIL method)
$3n \cdot 6n + 3n \cdot 2 + 7 \cdot 6n + 7 \cdot 2$
## Step 2: Simplify each term
$18n^2 + 6n + 42n + 14$
## Step 3: Combine like terms
$6n + 42n = 48n$
# Answer:
$18n^2 + 48n + 14$

### Problem 7: Find the product $(8n - 1)(4n + 2)$
# Explanation:
## Step 1: Use the distributive property (FOIL method)
$8n \cdot 4n + 8n \cdot 2 - 1 \cdot 4n - 1 \cdot 2$
## Step 2: Simplify each term
$32n^2 + 16n - 4n - 2$
## Step 3: Combine like terms
$16n - 4n = 12n$
# Answer:
$32n^2 + 12n - 2$

### Problem 8: Factor $k^2 + 9k + 20$ completely
# Explanation:
## Step 1: Find two numbers that multiply to $20$ and add to $9$
The numbers are $4$ and $5$ (since $4 \times 5 = 20$ and $4 + 5 = 9$)
## Step 2: Write the factored form
$(k + 4)(k + 5)$
# Answer:
$(k + 4)(k + 5)$

### Problem 9: Factor $v^2 + 10v + 9$ completely
# Explanation:
## Step 1: Find two numbers that multiply to $9$ and add to $10$
The numbers are $1$ and $9$ (since $1 \times 9 = 9$ and $1 + 9 = 10$)
## Step 2: Write the factored form
$(v + 1)(v + 9)$
# Answer:
$(v + 1)(v + 9)$

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QUESTION IMAGE

Question

Explanation:

Problem 1: Simplify \((7x^4 - x^3 - 6x) + (6x^4 - 8x + 4x^3)\)

Step 1: Combine like terms for \(x^4\)

Step 2: Combine like terms for \(x^3\)

Step 3: Combine like terms for \(x\)

Step 1: Combine like terms for \(x^3\)

Step 2: Combine like terms for \(x^2\)

Step 3: Combine like terms for \(x\)

Step 1: Distribute the negative sign

Step 2: Combine like terms for \(n^3\)

Step 3: Combine like terms for \(n^2\)

Step 4: Combine like terms for \(n\)

Answer:

Problem 2: Simplify \((7x^2 - 7x + 3x^3) + (6x^3 - 3x + 2x^2)\)