Could someone please help me solve the following problems, and show me how to do the work? I am getting confused, and need something to refer to when doing future problems. Thank you so much!

(6x+1)(x^2-9x+5)
(2x^4+3)(4x^3+2)
(12y^3+8y^2+20y) div. by 2y
(6x^2-25x-10) div. by (3x +2)
(8x-5)+(7x+4)
(5x-3.6)-(4x+1.2)
(3x^2+3x)+(4x+(6x-6)-(3x-3)

See your 3:30am post for solutions.

Sure! I'd be happy to help you solve these problems and explain the steps involved.

1. (6x+1)(x^2-9x+5)
To simplify this expression, you can use the distributive property. Start by multiplying each term of the first factor (6x + 1) by each term of the second factor (x^2 - 9x + 5):

(6x)(x^2) + (6x)(-9x) + (6x)(5) + (1)(x^2) + (1)(-9x) + (1)(5)

Simplify each product:

6x^3 - 54x^2 + 30x + x^2 - 9x + 5

Combine like terms:

6x^3 - 53x^2 + 21x + 5

So, the simplified expression is 6x^3 - 53x^2 + 21x + 5.

2. (2x^4 + 3)(4x^3 + 2)
Again, use the distributive property to simplify this expression:

(2x^4)(4x^3) + (2x^4)(2) + (3)(4x^3) + (3)(2)

Multiply each term:

8x^7 + 4x^4 + 12x^3 + 6

Combine like terms if applicable.

The simplified expression is 8x^7 + 4x^4 + 12x^3 + 6.

3. (12y^3 + 8y^2 + 20y) divided by 2y
To divide this expression by 2y, divide each term separately:

12y^3 / 2y + 8y^2 / 2y + 20y / 2y

Simplify each division by canceling out common factors:

6y^2 + 4y + 10

The simplified expression is 6y^2 + 4y + 10.

4. (6x^2 - 25x - 10) divided by (3x + 2)
To divide this expression, you can either use long division or synthetic division. Let's use long division for this example:

Start by dividing the first term of the dividend (6x^2) by the first term of the divisor (3x). The result is 2x. Multiply the entire divisor (3x + 2) by 2x, and subtract the result from the dividend.

2x - 3
_______________
3x + 2 | 6x^2 - 25x - 10
- (6x^2 + 4x)
_______________
-29x - 10

Now, continue dividing the remaining terms (-29x - 10) by the first term of the divisor (3x). The result is -10. Multiply the entire divisor by -10 and subtract the result from the previous step.

2x - 3 -10
_______________
3x + 2 | 6x^2 - 25x - 10
- (6x^2 + 4x)
_______________
-29x - 10
-(-29x - 20)
________________
10

The coefficient of the remainder is 10.

The simplified expression is 2x - 3 - 10/(3x + 2).

5. (8x - 5) + (7x + 4)
To simplify this expression, combine like terms:

8x + 7x - 5 + 4

Combine like terms:

15x - 1

The simplified expression is 15x - 1.

6. (5x - 3.6) - (4x + 1.2)
Again, combine like terms to simplify:

5x - 4x - 3.6 - 1.2

Combine like terms:

x - 4.8

The simplified expression is x - 4.8.

7. (3x^2 + 3x) + (4x + (6x - 6) - (3x - 3))
Start by simplifying the innermost parentheses:

3x^2 + 3x + 4x + (6x - 6) - (3x - 3)

Combine like terms:

3x^2 + 7x + (6x - 6) - (3x - 3)

Distribute the negative sign to the terms inside the second set of parentheses:

3x^2 + 7x + 6x - 6 - 3x + 3

Combine like terms:

3x^2 + 10x - 3

The simplified expression is 3x^2 + 10x - 3.

I hope these explanations help you understand how to solve these problems. If you have any further questions, please feel free to ask!