Question 1

Question

A)
Use the table to answer the question.

4x3 4x2
24x4 12x3 6x
- 36x3 -18x2 -9

A table is shown with 2 rows and 2 columns. The horizontal side is labeled 4 x cubed and 2 x squared while the vertical side is labeled 6 x and negative 9.

Find the product of (4x3+2x2)(6x−9). Provide your answer in descending order of exponents.

(1 point)
(4x3+2x2)(6x−9)=''blank''

Question 2
A)Complete the table to find the product of (5y2−6y)(7y7−y3). Provide your answer in descending order of exponents.(2 points)

5y2 -6y
blank blank 7y7
blank blank -y3
(5y2-6y) (7y7-y3) = ''blank''

Question 3
A)Use the Distributive Property to multiply the following polynomials: 3x2(2x4−15x).(1 point)

3x2(2x4−15x)= ''blank''

Question 4
A)Find the product of (3x2−8)(4x2+7). Provide your answer in descending order of exponents.(1 point)

(3x2−8)(4x2+7)= ''blank''

Question 5
A)What is the product of the following polynomials: (−3x5−4x4)(7x2−2x+6)?(1 point)

(−3x5−4x4)(7x2−2x+6)= ''blank''

Answer 1

Sure! Let's go through each question one by one and calculate the requested products.

Question 1

To find the product \((4x^3 + 2x^2)(6x - 9)\), we will use the distributive property (also called the FOIL method for binomials).

1. \(4x^3(6x) = 24x^4\)
2. \(4x^3(-9) = -36x^3\)
3. \(2x^2(6x) = 12x^3\)
4. \(2x^2(-9) = -18x^2\)

Now, we combine these results: \[ (4x^3 + 2x^2)(6x - 9) = 24x^4 + (-36x^3 + 12x^3) + (-18x^2) = 24x^4 - 24x^3 - 18x^2 \]

Thus, \[ (4x^3 + 2x^2)(6x - 9) = 24x^4 - 24x^3 - 18x^2 \]

Question 2

We need to fill in the table for \((5y^2 - 6y)(7y^7 - y^3)\).

Using distribution:

1. \(5y^2(7y^7) = 35y^9\)
2. \(5y^2(-y^3) = -5y^5\)
3. \(-6y(7y^7) = -42y^8\)
4. \(-6y(-y^3) = 6y^4\)

Now, we combine: \[ (5y^2 - 6y)(7y^7 - y^3) = 35y^9 - 42y^8 - 5y^5 + 6y^4 \]

Thus, \[ (5y^2 - 6y)(7y^7 - y^3) = 35y^9 - 42y^8 - 5y^5 + 6y^4 \]

Question 3

Using the Distributive Property to multiply \(3x^2(2x^4 - 15x)\):

1. \(3x^2(2x^4) = 6x^6\)
2. \(3x^2(-15x) = -45x^3\)

So, \[ 3x^2(2x^4 - 15x) = 6x^6 - 45x^3 \]

Question 4

Now we need to compute \((3x^2 - 8)(4x^2 + 7)\):

1. \(3x^2(4x^2) = 12x^4\)
2. \(3x^2(7) = 21x^2\)
3. \(-8(4x^2) = -32x^2\)
4. \(-8(7) = -56\)

Combining: \[ (3x^2 - 8)(4x^2 + 7) = 12x^4 + (21x^2 - 32x^2) - 56 = 12x^4 - 11x^2 - 56 \]

Question 5

Now we will find the product of \((-3x^5 - 4x^4)(7x^2 - 2x + 6)\):

1. \(-3x^5(7x^2) = -21x^7\)
2. \(-3x^5(-2x) = 6x^6\)
3. \(-3x^5(6) = -18x^5\)
4. \(-4x^4(7x^2) = -28x^6\)
5. \(-4x^4(-2x) = 8x^5\)
6. \(-4x^4(6) = -24x^4\)

Now we combine all the terms: \[ -21x^7 + (6x^6 - 28x^6) + (-18x^5 + 8x^5) - 24x^4 = -21x^7 - 22x^6 - 10x^5 - 24x^4 \]

Summary of Answers

1. \( (4x^3 + 2x^2)(6x - 9) = 24x^4 - 24x^3 - 18x^2 \)

2. \( (5y^2 - 6y)(7y^7 - y^3) = 35y^9 - 42y^8 - 5y^5 + 6y^4 \)

3. \( 3x^2(2x^4 - 15x) = 6x^6 - 45x^3 \)

4. \( (3x^2 - 8)(4x^2 + 7) = 12x^4 - 11x^2 - 56 \)

5. \( (-3x^5 - 4x^4)(7x^2 - 2x + 6) = -21x^7 - 22x^6 - 10x^5 - 24x^4 \)