set 2 simplify each expression. then, find the difference of your answers in each row.
1 (7x + 3)(x - 9)
(5x + 3)(x + 1)
8 (2x + 1)(2x - 1)
(x + 4)(x - 4)
9 (4x + 1)(3x - 7)
(3x - 4)(2x - 8)
10 (3x - 1)^2
(x + 6)^2
11 (x - 2)(x^2 + 8x - 1)
(x + 4)(x^2 - 5x + 9)
12 (3x + 5)(x^2 - 10x + 2)
(2x - 1)(x^2 - 3x - 7)

Question

Accepted Answer

Let's solve one of the problems, say problem 1: $(7x + 3)(x - 9)$ and $(5x + 3)(x + 1)$, then find their difference.

### Step 1: Expand $(7x + 3)(x - 9)$
Using the distributive property (FOIL method):
$$
\begin{align*}
(7x + 3)(x - 9)&=7x\cdot x+7x\cdot(-9)+3\cdot x + 3\cdot(-9)\
&=7x^{2}-63x + 3x-27\
&=7x^{2}-60x - 27
\end{align*}
$$

### Step 2: Expand $(5x + 3)(x + 1)$
Using the distributive property (FOIL method):
$$
\begin{align*}
(5x + 3)(x + 1)&=5x\cdot x+5x\cdot1+3\cdot x+3\cdot1\
&=5x^{2}+5x + 3x + 3\
&=5x^{2}+8x + 3
\end{align*}
$$

### Step 3: Find the difference $(7x^{2}-60x - 27)-(5x^{2}+8x + 3)$
Subtract the second expanded form from the first:
$$
\begin{align*}
&(7x^{2}-60x - 27)-(5x^{2}+8x + 3)\
=&7x^{2}-60x - 27 - 5x^{2}-8x - 3\
=&(7x^{2}-5x^{2})+(-60x-8x)+(-27 - 3)\
=&2x^{2}-68x - 30
\end{align*}
$$

Let's solve problem 8: $(2x + 1)(2x - 1)$ and $(x + 4)(x - 4)$, then find their difference.

### Step 1: Expand $(2x + 1)(2x - 1)$
Using the difference of squares formula $(a + b)(a - b)=a^{2}-b^{2}$, where $a = 2x$ and $b = 1$:
$$
(2x + 1)(2x - 1)=(2x)^{2}-1^{2}=4x^{2}-1
$$

### Step 2: Expand $(x + 4)(x - 4)$
Using the difference of squares formula $(a + b)(a - b)=a^{2}-b^{2}$, where $a=x$ and $b = 4$:
$$
(x + 4)(x - 4)=x^{2}-4^{2}=x^{2}-16
$$

### Step 3: Find the difference $(4x^{2}-1)-(x^{2}-16)$
Subtract the second expanded form from the first:
$$
\begin{align*}
&(4x^{2}-1)-(x^{2}-16)\
=&4x^{2}-1 - x^{2}+16\
=&(4x^{2}-x^{2})+(-1 + 16)\
=&3x^{2}+15
\end{align*}
$$

Let's solve problem 9: $(4x + 1)(3x - 7)$ and $(3x - 4)(2x - 8)$, then find their difference.

### Step 1: Expand $(4x + 1)(3x - 7)$
Using the distributive property:
$$
\begin{align*}
(4x + 1)(3x - 7)&=4x\cdot3x+4x\cdot(-7)+1\cdot3x + 1\cdot(-7)\
&=12x^{2}-28x+3x - 7\
&=12x^{2}-25x - 7
\end{align*}
$$

### Step 2: Expand $(3x - 4)(2x - 8)$
Using the distributive property:
$$
\begin{align*}
(3x - 4)(2x - 8)&=3x\cdot2x+3x\cdot(-8)-4\cdot2x-4\cdot(-8)\
&=6x^{2}-24x-8x + 32\
&=6x^{2}-32x + 32
\end{align*}
$$

### Step 3: Find the difference $(12x^{2}-25x - 7)-(6x^{2}-32x + 32)$
Subtract the second expanded form from the first:
$$
\begin{align*}
&(12x^{2}-25x - 7)-(6x^{2}-32x + 32)\
=&12x^{2}-25x - 7 - 6x^{2}+32x - 32\
=&(12x^{2}-6x^{2})+(-25x + 32x)+(-7 - 32)\
=&6x^{2}+7x - 39
\end{align*}
$$

Let's solve problem 10: $(3x - 1)^{2}$ and $(x + 6)^{2}$, then find their difference.

### Step 1: Expand $(3x - 1)^{2}$
Using the perfect square formula $(a - b)^{2}=a^{2}-2ab + b^{2}$, where $a = 3x$ and $b = 1$:
$$
(3x - 1)^{2}=(3x)^{2}-2\cdot3x\cdot1+1^{2}=9x^{2}-6x + 1
$$

### Step 2: Expand $(x + 6)^{2}$
Using the perfect square formula $(a + b)^{2}=a^{2}+2ab + b^{2}$, where $a=x$ and $b = 6$:
$$
(x + 6)^{2}=x^{2}+2\cdot x\cdot6+6^{2}=x^{2}+12x + 36
$$

### Step 3: Find the difference $(9x^{2}-6x + 1)-(x^{2}+12x + 36)$
Subtract the second expanded form from the first:
$$
\begin{align*}
&(9x^{2}-6x + 1)-(x^{2}+12x + 36)\
=&9x^{2}-6x + 1 - x^{2}-12x - 36\
=&(9x^{2}-x^{2})+(-6x-12x)+(1 - 36)\
=&8x^{2}-18x - 35
\end{align*}
$$

Let's solve problem 11: $(x - 2)(x^{2}+8x - 1)$ and $(x + 4)(x^{2}-5x + 9)$, then find their difference.

### Step 1: Expand $(x - 2)(x^{2}+8x - 1)$
Using the distributive property:
$$
\begin{align*}
&x(x^{2}+8x - 1)-2(x^{2}+8x - 1)\
=&x^{3}+8x^{2}-x-2x^{2}-16x + 2\
=&x^{3}+(8x^{2}-2x^{2})+(-x-16x)+2\
=&x^{3}+6x^{2}-17x + 2
\end{align*}
$$

### Step 2: Expand $(x + 4)(x^{2}-5x + 9)$
Using the distributive property:
$$
\begin{align*}
&x(x^{2}-5x + 9)+4(x^{2}-5x + 9)\
=&x^{3}-5x^{2}+9x + 4x^{2}-20x + 36\
=&x^{3}+(-5x^{2}+4x^{2})+(9x-20x)+36\
=&x^{3}-x^{2}-11x + 36
\end{align*}
$$

### Step 3: Find the difference $(x^{3}+6x^{2}-17x + 2)-(x^{3}-x^{2}-11x + 36)$
Subtract the second expanded form from the first:
$$
\begin{align*}
&(x^{3}+6x^{2}-17x + 2)-(x^{3}-x^{2}-11x + 36)\
=&x^{3}+6x^{2}-17x + 2 - x^{3}+x^{2}+11x - 36\
=&(x^{3}-x^{3})+(6x^{2}+x^{2})+(-17x + 11x)+(2 - 36)\
=&7x^{2}-6x - 34
\end{align*}
$$

Let's solve problem 12: $(3x + 5)(x^{2}-10x + 2)$ and $(2x - 1)(x^{2}-3x - 7)$, then find their difference.

### Step 1: Expand $(3x + 5)(x^{2}-10x + 2)$
Using the distributive property:
$$
\begin{align*}
&3x(x^{2}-10x + 2)+5(x^{2}-10x + 2)\
=&3x^{3}-30x^{2}+6x+5x^{2}-50x + 10\
=&3x^{3}+(-30x^{2}+5x^{2})+(6x-50x)+10\
=&3x^{3}-25x^{2}-44x + 10
\end{align*}
$$

### Step 2: Expand $(2x - 1)(x^{2}-3x - 7)$
Using the distributive property:
$$
\begin{align*}
&2x(x^{2}-3x - 7)-1(x^{2}-3x - 7)\
=&2x^{3}-6x^{2}-14x-x^{2}+3x + 7\
=&2x^{3}+(-6x^{2}-x^{2})+(-14x + 3x)+7\
=&2x^{3}-7x^{2}-11x + 7
\end{align*}
$$

### Step 3: Find the difference $(3x^{3}-25x^{2}-44x + 10)-(2x^{3}-7x^{2}-11x + 7)$
Subtract the second expanded form from the first:
$$
\begin{align*}
&(3x^{3}-25x^{2}-44x + 10)-(2x^{3}-7x^{2}-11x + 7)\
=&3x^{3}-25x^{2}-44x + 10 - 2x^{3}+7x^{2}+11x - 7\
=&(3x^{3}-2x^{3})+(-25x^{2}+7x^{2})+(-44x + 11x)+(10 - 7)\
=&x^{3}-18x^{2}-33x + 3
\end{align*}
$$

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QUESTION IMAGE

Question

Explanation:

Step 1: Expand \((7x + 3)(x - 9)\)

Step 2: Expand \((5x + 3)(x + 1)\)

Step 3: Find the difference \((7x^{2}-60x - 27)-(5x^{2}+8x + 3)\)

Step 1: Expand \((2x + 1)(2x - 1)\)

Step 2: Expand \((x + 4)(x - 4)\)

Step 3: Find the difference \((4x^{2}-1)-(x^{2}-16)\)

Step 1: Expand \((4x + 1)(3x - 7)\)

Step 2: Expand \((3x - 4)(2x - 8)\)

Step 3: Find the difference \((12x^{2}-25x - 7)-(6x^{2}-32x + 32)\)

Step 1: Expand \((3x - 1)^{2}\)

Step 2: Expand \((x + 6)^{2}\)

Step 3: Find the difference \((9x^{2}-6x + 1)-(x^{2}+12x + 36)\)

Step 1: Expand \((x - 2)(x^{2}+8x - 1)\)

Step 2: Expand \((x + 4)(x^{2}-5x + 9)\)

Answer: