practice concepts from previous topics. 1 rewrite each expression using multiplication. a (3 - 2i)(4 + 5i) b (7 - 6i)² 2 add or subtract the expressions given. a (4x² - 2x + 7) + (-8x² + 5x - 25) b (-9x² + 16x - 17) - (-12x² - 7 3 dilate each function by the given factor to create a new function of higher degre sketch the graph and then identify the zeros of the new function. a f(x) = (x + 3)(4x - 1) dilate by (x - 1). b f(x) = (x + 2)(x - 2) dilate by x.

Question

Accepted Answer

### Problem 1a:
# Explanation:
## Step1: Apply distributive property (FOIL)
$(3 - 2i)(4 + 5i)=3	imes4 + 3	imes5i-2i	imes4-2i	imes5i$
## Step2: Simplify each term
$=12 + 15i-8i - 10i^2$
## Step3: Recall $i^2 = -1$
$=12 + 7i-10	imes(-1)$
## Step4: Simplify further
$=12 + 7i + 10=22 + 7i$
# Answer:
$22 + 7i$

### Problem 1b:
# Explanation:
## Step1: Expand the square
$(7 - 6i)^2=(7 - 6i)(7 - 6i)$
## Step2: Apply distributive property (FOIL)
$=7	imes7-7	imes6i-6i	imes7 + 36i^2$
## Step3: Simplify each term
$=49-42i-42i + 36i^2$
## Step4: Recall $i^2=-1$
$=49-84i + 36	imes(-1)$
## Step5: Simplify further
$=49-84i-36 = 13-84i$
# Answer:
$13-84i$

### Problem 2a:
# Explanation:
## Step1: Remove parentheses
$(4x^2-2x + 7)+(-8x^2 + 5x-25)=4x^2-2x + 7-8x^2 + 5x-25$
## Step2: Combine like terms
$=(4x^2-8x^2)+(-2x + 5x)+(7-25)$
## Step3: Simplify each group
$=-4x^2 + 3x-18$
# Answer:
$-4x^2 + 3x-18$

### Problem 2b: (Assuming the second expression is $(-9x^2 + 16x-17)-(-12x^2-7x + c)$ (missing term assumed as $+0$ for $x$ and some constant, but let's proceed with given visible part))
# Explanation:
## Step1: Remove parentheses (distribute the negative)
$(-9x^2 + 16x-17)-(-12x^2-7x)=-9x^2 + 16x-17 + 12x^2 + 7x$
## Step2: Combine like terms
$=(-9x^2 + 12x^2)+(16x + 7x)-17$
## Step3: Simplify each group
$=3x^2 + 23x-17$ (If there was a constant term, we would combine that too, but with given info, this is the result)
# Answer:
$3x^2 + 23x-17$ (adjust if the missing term is known)

### Problem 3a:
# Explanation:
## Step1: Dilation means multiply the function by the factor $(x - 1)$
New function $g(x)=(x - 1)	imes f(x)=(x - 1)(x + 3)(4x-1)$
## Step2: First multiply $(x - 1)(x + 3)$
$=(x^2+3x-x - 3)=(x^2 + 2x-3)$
## Step3: Now multiply by $(4x-1)$
$=(x^2 + 2x-3)(4x-1)=4x^3-x^2 + 8x^2-2x-12x + 3$
## Step4: Combine like terms
$=4x^3+( -x^2 + 8x^2)+(-2x-12x)+3$
## Step5: Simplify
$=4x^3 + 7x^2-14x + 3$
## Step6: Find zeros by setting $g(x)=0$
$(x - 1)(x + 3)(4x-1)=0$
So zeros are $x = 1,x=-3,x=\frac{1}{4}$
# Answer:
New function: $4x^3 + 7x^2-14x + 3$; Zeros: $x = 1,x=-3,x=\frac{1}{4}$

### Problem 3b:
# Explanation:
## Step1: Dilation means multiply the function by the factor $x$
New function $g(x)=x	imes f(x)=x(x + 2)(x - 2)$
## Step2: Simplify $(x + 2)(x - 2)=x^2-4$ (difference of squares)
## Step3: Multiply by $x$
$g(x)=x(x^2-4)=x^3-4x$
## Step4: Find zeros by setting $g(x)=0$
$x(x^2-4)=0\Rightarrow x(x - 2)(x + 2)=0$
So zeros are $x = 0,x = 2,x=-2$
# Answer:
New function: $x^3-4x$; Zeros: $x = 0,x = 2,x=-2$

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QUESTION IMAGE

Question

Explanation:

Problem 1a:

Step1: Apply distributive property (FOIL)

Step2: Simplify each term

Step3: Recall $i^2 = -1$

Step4: Simplify further

Step1: Expand the square

Step2: Apply distributive property (FOIL)

Step3: Simplify each term

Step4: Recall $i^2=-1$

Step5: Simplify further

Step1: Remove parentheses

Step2: Combine like terms

Step3: Simplify each group

Answer:

Problem 1b: