Question
What is the simplest form of (4x3 + 6x – 7) + (3x3 – 5x2 – 5x + 9)?
A. 7x3 – 5x2 – x + 2
B. 7x3 – 5x2 + x + 2
C. 7x3 + x2 – 5x + 2
D. 7x6 – 4x2 + 2
Which of the following is (−5x + 4) − (3x2 − 7x + 4) simplified and written in standard form?
A. 3x2 − 12x + 8
B. 2x − 3x2
C. −3x2 + 7x − 5x
D. −3x2 + 2x
Choose the product of –3y2(–4y3 + y – 9).
A. –7y5 – 3y3 – 27y2
B. 12y6 – 3y2 + 27y2
C. 12y6 – 3y2 + 12y2
D. 12y5 – 3y3 + 27y2
Which of the following is the product of (7x + 2) and (5x − 11)?
A. 12x2 − 10x − 77x − 22
B. 35x2 − 67x − 22
C. 12x2 − 67x − 22
D. 35x2 + 67x + 22
Maime is painting a rectangular wall in her bedroom and stringing lights along its edges. The dimensions of the wall are (y + 3) feet by (2y + 5) feet.
Part A
Which expressions represent the area of the wall to be painted? Select all that apply.
A. 2y2 + 5y + 6y + 15
B. y + 3 + (2y + 5)
C. (y + 3)(2y + 5)
D. 2y2 + 10y + 15
E. 2y2 + 11y + 15
F. 2y2 + 11y + 8
Part B
How many feet of lights does Maime need to string along the wall? Write your answer in standard form.
y +
Write the product in standard form. (3a − 4) 2a2 − 1 + 5a
a3 −
a2 −
a +
Simplify the expression.
(8w3 − 6w2 + 4) − (7w + 2w3 − 1)
A. 6w3 − 6w2 − 7w + 3
B. 6w3 − 6w2 − 7w + 5
C. 10w3 − 6w2 + 7w + 3
D. 10w3 − 6w2 − 7w + 3
A. 7x3 – 5x2 – x + 2
B. 7x3 – 5x2 + x + 2
C. 7x3 + x2 – 5x + 2
D. 7x6 – 4x2 + 2
Which of the following is (−5x + 4) − (3x2 − 7x + 4) simplified and written in standard form?
A. 3x2 − 12x + 8
B. 2x − 3x2
C. −3x2 + 7x − 5x
D. −3x2 + 2x
Choose the product of –3y2(–4y3 + y – 9).
A. –7y5 – 3y3 – 27y2
B. 12y6 – 3y2 + 27y2
C. 12y6 – 3y2 + 12y2
D. 12y5 – 3y3 + 27y2
Which of the following is the product of (7x + 2) and (5x − 11)?
A. 12x2 − 10x − 77x − 22
B. 35x2 − 67x − 22
C. 12x2 − 67x − 22
D. 35x2 + 67x + 22
Maime is painting a rectangular wall in her bedroom and stringing lights along its edges. The dimensions of the wall are (y + 3) feet by (2y + 5) feet.
Part A
Which expressions represent the area of the wall to be painted? Select all that apply.
A. 2y2 + 5y + 6y + 15
B. y + 3 + (2y + 5)
C. (y + 3)(2y + 5)
D. 2y2 + 10y + 15
E. 2y2 + 11y + 15
F. 2y2 + 11y + 8
Part B
How many feet of lights does Maime need to string along the wall? Write your answer in standard form.
y +
Write the product in standard form. (3a − 4) 2a2 − 1 + 5a
a3 −
a2 −
a +
Simplify the expression.
(8w3 − 6w2 + 4) − (7w + 2w3 − 1)
A. 6w3 − 6w2 − 7w + 3
B. 6w3 − 6w2 − 7w + 5
C. 10w3 − 6w2 + 7w + 3
D. 10w3 − 6w2 − 7w + 3
Answers
GPT-4o mini
Let's go through each of the questions one at a time:
### Question 1
**Simplifying (4x³ + 6x - 7) + (3x³ - 5x² - 5x + 9)**
Combine like terms:
1. Combine \(x³\) terms: \(4x³ + 3x³ = 7x³\)
2. Combine \(x²\) terms: \(0 - 5x² = -5x²\)
3. Combine \(x\) terms: \(6x - 5x = x\)
4. Combine constant terms: \(-7 + 9 = 2\)
Putting it all together, we have:
**Answer: A. 7x³ - 5x² + x + 2**
### Question 2
**Simplifying (−5x + 4) − (3x² − 7x + 4)**
Distribute the negative:
1. \(−5x + 4 - 3x² + 7x - 4\)
Now combine like terms:
1. Combine \(x²\) terms: \(−3x²\)
2. Combine \(x\) terms: \(-5x + 7x = 2x\)
3. Combine constant terms: \(4 - 4 = 0\)
Putting it all together, we have:
**Answer: D. -3x² + 2x**
### Question 3
**Finding the product of –3y²(–4y³ + y – 9)**
Distributing:
1. \(−3y²(−4y³) = 12y^{5}\)
2. \(−3y²(y) = -3y^{3}\)
3. \(−3y²(−9) = 27y²\)
Putting it all together, we get:
**Answer: D. 12y^{5} - 3y^{3} + 27y²**
### Question 4
**Finding the product of (7x + 2) and (5x − 11)**
Using the distributive property (FOIL):
1. \(7x * 5x = 35x²\)
2. \(7x * -11 = -77x\)
3. \(2 * 5x = 10x\)
4. \(2 * -11 = -22\)
Combine like terms:
- \(-77x + 10x = -67x\)
Putting it all together, we have:
**Answer: B. 35x² - 67x - 22**
### Question 5 Part A
**Finding the area of the wall represented by (y + 3) and (2y + 5)**
The area is given by:
\[ A = (y + 3)(2y + 5) \]
Calculating the area:
1. \(y \cdot 2y = 2y²\)
2. \(y \cdot 5 = 5y\)
3. \(3 \cdot 2y = 6y\)
4. \(3 \cdot 5 = 15\)
Combine them: \(2y² + 5y + 6y + 15 = 2y² + 11y + 15\)
The expressions that represent the area:
- \((y + 3)(2y + 5)\)
- \(2y² + 11y + 15\)
So the answers are: **C, D, and E**
### Question 5 Part B
To find the perimeter:
\[ P = 2 \cdot (length + width) = 2 \cdot [(y + 3) + (2y + 5)] = 2 \cdot (3y + 8) = 6y + 16 \]
Thus, Maime needs to string:
**Answer: 6y + 16 feet of lights**
### Question 6
**Finding the product in standard form of (3a − 4)(2a² − 1) + 5a**
1. \(3a \cdot 2a² = 6a³\)
2. \(3a \cdot -1 = -3a\)
3. \(-4 \cdot 2a² = -8a²\)
4. \(-4 \cdot -1 = 4\)
Putting it together gives:
\[ 6a³ - 8a² - 3a + 4 + 5a = 6a³ - 8a² + 2a + 4 \]
Final expression is:
**Answer: 6a³ - 8a² + 2a + 4**
### Question 7
**Simplifying (8w³ − 6w² + 4) − (7w + 2w³ − 1)**
Distributing the negative:
1. \(8w³ - 6w² + 4 - 7w - 2w³ + 1\)
Now combine like terms:
1. \(8w³ - 2w³ = 6w³\)
2. \(-6w²\) has no like term.
3. \(-7w\) has no like term.
4. \(4 + 1 = 5\)
Putting it all together gives:
**Answer: B. 6w³ - 6w² - 7w + 5**
### Question 1
**Simplifying (4x³ + 6x - 7) + (3x³ - 5x² - 5x + 9)**
Combine like terms:
1. Combine \(x³\) terms: \(4x³ + 3x³ = 7x³\)
2. Combine \(x²\) terms: \(0 - 5x² = -5x²\)
3. Combine \(x\) terms: \(6x - 5x = x\)
4. Combine constant terms: \(-7 + 9 = 2\)
Putting it all together, we have:
**Answer: A. 7x³ - 5x² + x + 2**
### Question 2
**Simplifying (−5x + 4) − (3x² − 7x + 4)**
Distribute the negative:
1. \(−5x + 4 - 3x² + 7x - 4\)
Now combine like terms:
1. Combine \(x²\) terms: \(−3x²\)
2. Combine \(x\) terms: \(-5x + 7x = 2x\)
3. Combine constant terms: \(4 - 4 = 0\)
Putting it all together, we have:
**Answer: D. -3x² + 2x**
### Question 3
**Finding the product of –3y²(–4y³ + y – 9)**
Distributing:
1. \(−3y²(−4y³) = 12y^{5}\)
2. \(−3y²(y) = -3y^{3}\)
3. \(−3y²(−9) = 27y²\)
Putting it all together, we get:
**Answer: D. 12y^{5} - 3y^{3} + 27y²**
### Question 4
**Finding the product of (7x + 2) and (5x − 11)**
Using the distributive property (FOIL):
1. \(7x * 5x = 35x²\)
2. \(7x * -11 = -77x\)
3. \(2 * 5x = 10x\)
4. \(2 * -11 = -22\)
Combine like terms:
- \(-77x + 10x = -67x\)
Putting it all together, we have:
**Answer: B. 35x² - 67x - 22**
### Question 5 Part A
**Finding the area of the wall represented by (y + 3) and (2y + 5)**
The area is given by:
\[ A = (y + 3)(2y + 5) \]
Calculating the area:
1. \(y \cdot 2y = 2y²\)
2. \(y \cdot 5 = 5y\)
3. \(3 \cdot 2y = 6y\)
4. \(3 \cdot 5 = 15\)
Combine them: \(2y² + 5y + 6y + 15 = 2y² + 11y + 15\)
The expressions that represent the area:
- \((y + 3)(2y + 5)\)
- \(2y² + 11y + 15\)
So the answers are: **C, D, and E**
### Question 5 Part B
To find the perimeter:
\[ P = 2 \cdot (length + width) = 2 \cdot [(y + 3) + (2y + 5)] = 2 \cdot (3y + 8) = 6y + 16 \]
Thus, Maime needs to string:
**Answer: 6y + 16 feet of lights**
### Question 6
**Finding the product in standard form of (3a − 4)(2a² − 1) + 5a**
1. \(3a \cdot 2a² = 6a³\)
2. \(3a \cdot -1 = -3a\)
3. \(-4 \cdot 2a² = -8a²\)
4. \(-4 \cdot -1 = 4\)
Putting it together gives:
\[ 6a³ - 8a² - 3a + 4 + 5a = 6a³ - 8a² + 2a + 4 \]
Final expression is:
**Answer: 6a³ - 8a² + 2a + 4**
### Question 7
**Simplifying (8w³ − 6w² + 4) − (7w + 2w³ − 1)**
Distributing the negative:
1. \(8w³ - 6w² + 4 - 7w - 2w³ + 1\)
Now combine like terms:
1. \(8w³ - 2w³ = 6w³\)
2. \(-6w²\) has no like term.
3. \(-7w\) has no like term.
4. \(4 + 1 = 5\)
Putting it all together gives:
**Answer: B. 6w³ - 6w² - 7w + 5**