Simplify the following expression

2(3 x - 2)(2nd Power) - 3x (x + 1) + 4

expand the first term and the second term

2(9x^2-12x+4)-3x^2-3x + 4
18x^2-24x+8-3x^2-3x+4
gather terms
15x^2-27x+12
(3x-3)(5x-4)
check that.

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

2 (9x^2 - 12 x +4) - 3 x^2 -3x + 4

18 x^2 - 24 x + 8 - 3x^2 -3x + 4

15 x^2 -27 x + 12
or
3(5 x^2 - 9 x + 4)

Oh, you can factor more

3(5 x^2 - 9 x + 4)
3 (5x-4)(x-1)

To simplify the expression: 2(3x - 2)^2 - 3x(x + 1) + 4, we need to follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

1. Start by simplifying what's inside the parentheses. We have (3x - 2) to the power of 2.

(3x - 2)^2 = (3x - 2)(3x - 2)
= 9x^2 - 6x - 6x + 4
= 9x^2 - 12x + 4

2. Now let's simplify the second term, -3x(x + 1).
Multiply -3x by each term inside the parentheses.

-3x(x + 1) = -3x * x + (-3x) * 1
= -3x^2 - 3x

3. Finally, we simplify the last term, +4.

Now, let's put it all together:

2(3x - 2)^2 - 3x(x + 1) + 4
= 2(9x^2 - 12x + 4) - 3x^2 - 3x + 4
= 18x^2 - 24x + 8 - 3x^2 - 3x + 4

Since both x^2 terms have opposite signs, we can combine them:
= (18x^2 - 3x^2) + (-24x - 3x) + (8 + 4)
= 15x^2 - 27x + 12

After simplifying the expression 2(3x - 2)^2 - 3x(x + 1) + 4, we obtain 15x^2 - 27x + 12.