Consider the following expression.

3(x - 2) - 9(x**2 + 7 x + 4) - 5(x + 8)

(a) Simplify the expression.

3(x-2)-9(x^2+7x+4)-5(x+8)

3x-6-9x^2-63x-36-5x-40
-9x^2-65x-82

you have to know the distributive property in order to do this one.

x(a+b)= xa+xb

so first, to make it easier, separate it. Like this:
3(x-2)
-9(x**2+7x+4)
-5(x+8)

Lets start with 3(x-2) 3*x is 3x and 3*-2 is -6... 3x-6

-9*x**2 is -9x**2 and -9*7x is -63x and -9*4 is -36 so this is -9**2-63x-36

-5(x+8) -5*x+ =5x and -5*8+ -40!!!!!

so you add these together to get

3x-6-9x**2-63x-36-5x-40

then you have to add all the like monomials together, which hopefully you can do but i'll explain it nonetheless.

63x+3x-5x= -65x
-6-36-40= -82
then -9x**2

putting these together, we get...(drum roll please :P)

-9x**2-65x-82!!!!!!!!

im tired. hope this helped.

To simplify the expression, we need to apply the order of operations, which is also known as PEMDAS. This stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's simplify the expression step by step:

Step 1: Distribute the numbers and simplify within parentheses.

3(x - 2) - 9(x**2 + 7x + 4) - 5(x + 8)
= 3x - 6 - 9(x**2) - 9(7x) - 9(4) - 5x - 5(8)

Now, let's simplify further.

Step 2: Simplify the exponents.

= 3x - 6 - 9x**2 - 63x - 36 - 5x - 40

Step 3: Combine like terms.

Now, let's combine the terms with the same variables and exponents.

= 3x - 5x - 63x - 9x**2 + (-6 - 36 - 40)

= (-9x**2 - 65x) + (-82)

Step 4: Simplify further if possible.

= -9x**2 - 65x - 82

So, the simplified expression is -9x**2 - 65x - 82.