13) $(4p - 1)^2$
14) $(7x - 6)(5x + 6)$
15) $(6n + 3)(6n - 4)$
16) $(8n + 1)(6n - 3)$
17) $(6k + 5)(5k + 5)$
18) $(3x - 4)(4x + 3)$
19) $(4a + 2)(6a^2 - a + 2)$
20) $(7k - 3)(k^2 - 2k + 7)$
21) $(7r^2 - 6r - 6)(2r - 4)$
22) $(n^2 + 6n - 4)(2n - 4)$
23) $(6n^2 - 6n - 5)(7n^2 + 6n - 5)$

Question

Accepted Answer

Let's solve problem 13: $(4p - 1)^2$

# Explanation:
## Step 1: Recall the formula for squaring a binomial
The formula for $(a - b)^2$ is $a^2 - 2ab + b^2$. Here, $a = 4p$ and $b = 1$.
## Step 2: Apply the formula
First, calculate $a^2=(4p)^2 = 16p^2$.
Then, calculate $2ab = 2\times(4p)\times(1)=8p$.
Next, calculate $b^2=(1)^2 = 1$.
Now, substitute these into the formula: $(4p - 1)^2=16p^2-8p + 1$.

# Answer:
$16p^2 - 8p + 1$

Let's solve problem 14: $(7x - 6)(5x + 6)$

# Explanation:
## Step 1: Use the distributive property (FOIL method)
Multiply the First terms: $7x\times5x = 35x^2$.
Multiply the Outer terms: $7x\times6 = 42x$.
Multiply the Inner terms: $-6\times5x=-30x$.
Multiply the Last terms: $-6\times6=-36$.
## Step 2: Combine like terms
Combine the middle terms: $42x-30x = 12x$.
So, $(7x - 6)(5x + 6)=35x^2+12x - 36$.

# Answer:
$35x^2 + 12x - 36$

Let's solve problem 15: $(6n + 3)(6n - 4)$

# Explanation:
## Step 1: Use the distributive property (FOIL method)
First terms: $6n\times6n = 36n^2$.
Outer terms: $6n\times(-4)=-24n$.
Inner terms: $3\times6n = 18n$.
Last terms: $3\times(-4)=-12$.
## Step 2: Combine like terms
Combine the middle terms: $-24n + 18n=-6n$.
So, $(6n + 3)(6n - 4)=36n^2-6n - 12$.

# Answer:
$36n^2 - 6n - 12$

Let's solve problem 16: $(8n + 1)(6n - 3)$

# Explanation:
## Step 1: Use the distributive property (FOIL method)
First terms: $8n\times6n = 48n^2$.
Outer terms: $8n\times(-3)=-24n$.
Inner terms: $1\times6n = 6n$.
Last terms: $1\times(-3)=-3$.
## Step 2: Combine like terms
Combine the middle terms: $-24n+6n=-18n$.
So, $(8n + 1)(6n - 3)=48n^2-18n - 3$.

# Answer:
$48n^2 - 18n - 3$

Let's solve problem 17: $(6k + 5)(5k + 5)$

# Explanation:
## Step 1: Use the distributive property (FOIL method)
First terms: $6k\times5k = 30k^2$.
Outer terms: $6k\times5 = 30k$.
Inner terms: $5\times5k = 25k$.
Last terms: $5\times5 = 25$.
## Step 2: Combine like terms
Combine the middle terms: $30k + 25k=55k$.
So, $(6k + 5)(5k + 5)=30k^2+55k + 25$.

# Answer:
$30k^2 + 55k + 25$

Let's solve problem 18: $(3x - 4)(4x + 3)$

# Explanation:
## Step 1: Use the distributive property (FOIL method)
First terms: $3x\times4x = 12x^2$.
Outer terms: $3x\times3 = 9x$.
Inner terms: $-4\times4x=-16x$.
Last terms: $-4\times3=-12$.
## Step 2: Combine like terms
Combine the middle terms: $9x-16x=-7x$.
So, $(3x - 4)(4x + 3)=12x^2-7x - 12$.

# Answer:
$12x^2 - 7x - 12$

Let's solve problem 19: $(4a + 2)(6a^2 - a + 2)$

# Explanation:
## Step 1: Use the distributive property (multiply each term in the first polynomial by each term in the second polynomial)
Multiply $4a$ by each term: $4a\times6a^2=24a^3$, $4a\times(-a)=-4a^2$, $4a\times2 = 8a$.
Multiply $2$ by each term: $2\times6a^2 = 12a^2$, $2\times(-a)=-2a$, $2\times2 = 4$.
## Step 2: Combine like terms
Combine the $a^2$ terms: $-4a^2+12a^2 = 8a^2$.
Combine the $a$ terms: $8a-2a = 6a$.
So, $(4a + 2)(6a^2 - a + 2)=24a^3+8a^2+6a + 4$.

# Answer:
$24a^3 + 8a^2 + 6a + 4$

Let's solve problem 20: $(7k - 3)(k^2 - 2k + 7)$

# Explanation:
## Step 1: Use the distributive property (multiply each term in the first polynomial by each term in the second polynomial)
Multiply $7k$ by each term: $7k\times k^2=7k^3$, $7k\times(-2k)=-14k^2$, $7k\times7 = 49k$.
Multiply $-3$ by each term: $-3\times k^2=-3k^2$, $-3\times(-2k)=6k$, $-3\times7=-21$.
## Step 2: Combine like terms
Combine the $k^2$ terms: $-14k^2-3k^2=-17k^2$.
Combine the $k$ terms: $49k + 6k=55k$.
So, $(7k - 3)(k^2 - 2k + 7)=7k^3-17k^2+55k - 21$.

# Answer:
$7k^3 - 17k^2 + 55k - 21$

Let's solve problem 21: $(7r^2 - 6r - 6)(2r - 4)$

# Explanation:
## Step 1: Use the distributive property (multiply each term in the first polynomial by each term in the second polynomial)
Multiply $7r^2$ by each term: $7r^2\times2r = 14r^3$, $7r^2\times(-4)=-28r^2$.
Multiply $-6r$ by each term: $-6r\times2r=-12r^2$, $-6r\times(-4)=24r$.
Multiply $-6$ by each term: $-6\times2r=-12r$, $-6\times(-4)=24$.
## Step 2: Combine like terms
Combine the $r^2$ terms: $-28r^2-12r^2=-40r^2$.
Combine the $r$ terms: $24r-12r = 12r$.
So, $(7r^2 - 6r - 6)(2r - 4)=14r^3-40r^2+12r + 24$.

# Answer:
$14r^3 - 40r^2 + 12r + 24$

Let's solve problem 22: $(n^2 + 6n - 4)(2n - 4)$

# Explanation:
## Step 1: Use the distributive property (multiply each term in the first polynomial by each term in the second polynomial)
Multiply $n^2$ by each term: $n^2\times2n = 2n^3$, $n^2\times(-4)=-4n^2$.
Multiply $6n$ by each term: $6n\times2n = 12n^2$, $6n\times(-4)=-24n$.
Multiply $-4$ by each term: $-4\times2n=-8n$, $-4\times(-4)=16$.
## Step 2: Combine like terms
Combine the $n^2$ terms: $-4n^2+12n^2 = 8n^2$.
Combine the $n$ terms: $-24n-8n=-32n$.
So, $(n^2 + 6n - 4)(2n - 4)=2n^3+8n^2-32n + 16$.

# Answer:
$2n^3 + 8n^2 - 32n + 16$

Let's solve problem 23: $(6n^2 - 6n - 5)(7n^2 + 6n - 5)$

# Explanation:
## Step 1: Use the distributive property (multiply each term in the first polynomial by each term in the second polynomial)
Multiply $6n^2$ by each term: $6n^2\times7n^2 = 42n^4$, $6n^2\times6n=36n^3$, $6n^2\times(-5)=-30n^2$.
Multiply $-6n$ by each term: $-6n\times7n^2=-42n^3$, $-6n\times6n=-36n^2$, $-6n\times(-5)=30n$.
Multiply $-5$ by each term: $-5\times7n^2=-35n^2$, $-5\times6n=-30n$, $-5\times(-5)=25$.
## Step 2: Combine like terms
Combine the $n^3$ terms: $36n^3-42n^3=-6n^3$.
Combine the $n^2$ terms: $-30n^2-36n^2-35n^2=-101n^2$.
Combine the $n$ terms: $30n-30n = 0$.
So, $(6n^2 - 6n - 5)(7n^2 + 6n - 5)=42n^4-6n^3-101n^2 + 25$.

# Answer:
$42n^4 - 6n^3 - 101n^2 + 25$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step 1: Recall the formula for squaring a binomial

Step 2: Apply the formula

Step 1: Use the distributive property (FOIL method)

Step 2: Combine like terms

Step 1: Use the distributive property (FOIL method)

Step 2: Combine like terms

Answer: