11) $8x^3 + 27$
find each product by using square of sums.
13) $(x + 3)^2$
15) $(6x + 3y)^2$
find each product by using square of differences.
17) $(x - 2)^2$
19) $(2a - 3b)^2$

Question

Accepted Answer

### Problem 11: $8x^3 + 27$
# Explanation:
## Step1: Identify the formula
This is a sum of cubes. The formula for sum of cubes is $a^3 + b^3=(a + b)(a^2 - ab + b^2)$. Here, $8x^3=(2x)^3$ and $27 = 3^3$, so $a = 2x$ and $b = 3$.
## Step2: Apply the formula
Substitute $a = 2x$ and $b = 3$ into the formula:
$$
\begin{align*}
(2x)^3+3^3&=(2x + 3)((2x)^2-(2x)(3)+3^2)\
&=(2x + 3)(4x^2-6x + 9)
\end{align*}
$$
# Answer: $(2x + 3)(4x^2-6x + 9)$

### Problem 13: $(x + 3)^2$ (Square of Sums)
# Explanation:
## Step1: Recall the formula
The square of a sum formula is $(a + b)^2=a^2+2ab + b^2$. Here, $a=x$ and $b = 3$.
## Step2: Apply the formula
Substitute $a=x$ and $b = 3$ into the formula:
$$
\begin{align*}
(x + 3)^2&=x^2+2(x)(3)+3^2\
&=x^2+6x + 9
\end{align*}
$$
# Answer: $x^2+6x + 9$

### Problem 15: $(6x + 3y)^2$ (Square of Sums)
# Explanation:
## Step1: Recall the formula
The square of a sum formula is $(a + b)^2=a^2+2ab + b^2$. Here, $a = 6x$ and $b=3y$.
## Step2: Apply the formula
Substitute $a = 6x$ and $b = 3y$ into the formula:
$$
\begin{align*}
(6x+3y)^2&=(6x)^2+2(6x)(3y)+(3y)^2\
&=36x^2 + 36xy+9y^2
\end{align*}
$$
# Answer: $36x^2 + 36xy + 9y^2$

### Problem 17: $(x - 2)^2$ (Square of Differences)
# Explanation:
## Step1: Recall the formula
The square of a difference formula is $(a - b)^2=a^2-2ab + b^2$. Here, $a=x$ and $b = 2$.
## Step2: Apply the formula
Substitute $a=x$ and $b = 2$ into the formula:
$$
\begin{align*}
(x - 2)^2&=x^2-2(x)(2)+2^2\
&=x^2-4x + 4
\end{align*}
$$
# Answer: $x^2-4x + 4$

### Problem 19: $(2a - 3b)^2$ (Square of Differences)
# Explanation:
## Step1: Recall the formula
The square of a difference formula is $(a - b)^2=a^2-2ab + b^2$. Here, $a = 2a$ and $b=3b$.
## Step2: Apply the formula
Substitute $a = 2a$ and $b = 3b$ into the formula:
$$
\begin{align*}
(2a-3b)^2&=(2a)^2-2(2a)(3b)+(3b)^2\
&=4a^2-12ab + 9b^2
\end{align*}
$$
# Answer: $4a^2-12ab + 9b^2$

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QUESTION IMAGE

Question

Explanation:

Problem 11: \(8x^3 + 27\)

Step1: Identify the formula

Step2: Apply the formula

Step1: Recall the formula

Step2: Apply the formula

Step1: Recall the formula

Step2: Apply the formula

Answer:

Problem 13: \((x + 3)^2\) (Square of Sums)