evaluate these expressions if a = 1, b = 2, c = 3, and d = 4.
17. 15d = ______
18. (\frac{1}{2}ab^3d = ) ______
19. (4sqrt{c^2d} = ) ______
20. ((a + b) - (c - d) = ) ______
combine the terms that can be combined. indicate the others in descending powers of x or a.
21. 720 + 40 - 60 - 120 + 15 = ______
22. 25ab + 6a² - 3b² + 6 = ______
23. 3a + 2b - 3a + 1 - 3 = ______
24. (3x^2 - 2xy + 4x^2 - 3xy + y^2 = ) ______
25. 2x + x + 25y - y - 4 = ______
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Question

Accepted Answer

### Question 17: $ 15d $
# Explanation:
## Step1: Substitute $ d = 4 $ into the expression.
$ 15d = 15 \times 4 $
## Step2: Calculate the product.
$ 15 \times 4 = 60 $
# Answer:
$ 60 $

### Question 18: $ \frac{1}{2}ab^3d $
# Explanation:
## Step1: Substitute $ a = 1 $, $ b = 2 $, $ d = 4 $ into the expression.
$ \frac{1}{2} \times 1 \times 2^3 \times 4 $
## Step2: Calculate $ 2^3 $.
$ 2^3 = 8 $
## Step3: Multiply the numbers.
$ \frac{1}{2} \times 1 \times 8 \times 4 = \frac{1}{2} \times 32 = 16 $
# Answer:
$ 16 $

### Question 19: $ 4\sqrt{c^2d} $
# Explanation:
## Step1: Substitute $ c = 3 $, $ d = 4 $ into the expression.
$ 4\sqrt{3^2 \times 4} $
## Step2: Calculate $ 3^2 $ and the product inside the square root.
$ 3^2 = 9 $, $ 9 \times 4 = 36 $
## Step3: Take the square root of 36 and multiply by 4.
$ \sqrt{36} = 6 $, $ 4 \times 6 = 24 $
# Answer:
$ 24 $

### Question 20: $ (a + b) - (c - d) $
# Explanation:
## Step1: Substitute $ a = 1 $, $ b = 2 $, $ c = 3 $, $ d = 4 $ into the expression.
$ (1 + 2) - (3 - 4) $
## Step2: Calculate the values inside the parentheses.
$ 1 + 2 = 3 $, $ 3 - 4 = -1 $
## Step3: Subtract the two results.
$ 3 - (-1) = 3 + 1 = 4 $
# Answer:
$ 4 $

### Question 21: $ 720 + 40 - 60 - 120 + 15 $
# Explanation:
## Step1: Add and subtract from left to right.
$ 720 + 40 = 760 $
## Step2: Subtract 60 from 760.
$ 760 - 60 = 700 $
## Step3: Subtract 120 from 700.
$ 700 - 120 = 580 $
## Step4: Add 15 to 580.
$ 580 + 15 = 595 $
# Answer:
$ 595 $

### Question 22: $ 25ab + 6a^2 - 3b^2 + 6 $ (No like terms to combine, so it remains as is or we can note the terms. But if we just simplify the constants? Wait, no, the terms are $ 25ab $, $ 6a^2 $, $ -3b^2 $, $ 6 $. So the expression is already in simplified form with terms in descending powers of $ a $ (since $ a^2 $ has higher power than $ ab $, then $ b^2 $, then constant). Wait, the problem says "Combine the terms that can be combined. Indicate the others in descending powers of $ x $ or $ a $." So for this one, no like terms, so we arrange in descending powers of $ a $: $ 6a^2 + 25ab - 3b^2 + 6 $
# Explanation:
## Step1: Identify like terms. There are no like terms (terms with same variables and exponents).
## Step2: Arrange in descending powers of $ a $. The powers of $ a $ in each term: $ 6a^2 $ (power 2), $ 25ab $ (power 1), $ -3b^2 $ (power 0 for $ a $), $ 6 $ (power 0 for $ a $). So order is $ 6a^2 + 25ab - 3b^2 + 6 $
# Answer:
$ 6a^2 + 25ab - 3b^2 + 6 $

### Question 23: $ 3a + 2b - 3a + 1 - 3 $
# Explanation:
## Step1: Combine like terms for $ a $: $ 3a - 3a = 0 $
## Step2: Combine like terms for constants: $ 1 - 3 = -2 $
## Step3: The remaining term is $ 2b $, so combine all: $ 0 + 2b - 2 = 2b - 2 $
# Answer:
$ 2b - 2 $

### Question 24: $ 3x^2 - 2xy + 4x^2 - 3xy + y^2 $
# Explanation:
## Step1: Combine like terms for $ x^2 $: $ 3x^2 + 4x^2 = 7x^2 $
## Step2: Combine like terms for $ xy $: $ -2xy - 3xy = -5xy $
## Step3: The term $ y^2 $ remains. Arrange in descending powers of $ x $: $ 7x^2 - 5xy + y^2 $
# Answer:
$ 7x^2 - 5xy + y^2 $

### Question 25: $ 2x + x + 25y - y - 4 $
# Explanation:
## Step1: Combine like terms for $ x $: $ 2x + x = 3x $
## Step2: Combine like terms for $ y $: $ 25y - y = 24y $
## Step3: The constant term $ -4 $ remains. So the expression is $ 3x + 24y - 4 $
# Answer:
$ 3x + 24y - 4 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 17: \( 15d \)

Step1: Substitute \( d = 4 \) into the expression.

Step2: Calculate the product.

Step1: Substitute \( a = 1 \), \( b = 2 \), \( d = 4 \) into the expression.

Step2: Calculate \( 2^3 \).

Step3: Multiply the numbers.

Step1: Substitute \( c = 3 \), \( d = 4 \) into the expression.

Step2: Calculate \( 3^2 \) and the product inside the square root.

Step3: Take the square root of 36 and multiply by 4.

Answer:

Question 18: \( \frac{1}{2}ab^3d \)