Explain, in your own words, the step-by-step process to simplifying the expression below. Include the simplif?

Because you are subtracting the terms in the second parentheses from the first, you distribute the negative sign to all of the terms in the second parentheses:

6x^2 - 5 - 3x^2 - x - 7

Now you can combine terms which contain x to the same power (all the x^2 terms can be added/subtracted, as can the x terms, and the terms with no x in them)

6x^2 - 3x^2 - x - 5 - 7 =

3x^2 - x -12

There are no coefficients that can be factored out, and the expression cannot be further factored, so the final answer is 3x^2 - x -12

(6x^2 − 5) − (3x^2 + x + 7)

step 1: apples with apples

6x^2 - 5 - 3x^2 - x - 7

group together terms with the same "degree" (the exponent of the variable)

6x^2 - 3x^2 - x - 5 - 7

(6x^2 - 3x^2) - x - (5 + 7)

We can now add apples with apples, oranges with oranges.

3x^2 - x - 12

Next, we try to find the "roots" of this expression (values of x that will made the expression equal to zero).

In this case, it does not look easy, so we go to the "quadratic formula".

The expression is already written in the standard format of

ax^2 + bx + c

and the formula (a recipe) for the roots is:

x = [ -b +/- √( b^2 - 4ac ) ] / 2a

In this expression, the values are

a = 3

b = -1

c = -12

roots = [ +1 +/- √( 1 - 4(3)(-12) ) ] / 6

roots = [ 1 +/- √(145) ] / 6

One root is

[ 1 + √(145) ] / 6

the other root is

[ 1 - √145) ] / 6

The beauty of finding the roots is that once you have a root, then you can find the factors.

If "k" is a root, then (x-k) is a factor.

3x^2 - x - 12 = [x - 1 + √(145)] [x - 1 - √(145)]

Starting with (6x^2 - 5) - (3x^2 + x + 7)

Remove the brackets remembering to change the sign of the terms inside the second bracket because it is preceded by a minus:

= 6x^2 - 5 - 3x^2 - x - 7

Collect like terms:

= 6x^2 - 3x^2 - x - 5 - 7

Simplify like terms:

= 3x^2 - x - 12

(6x2 − 5) − (3x2 + x + 7)

change subtraction sign in middle to addition sign, and make all the signs in the second parenthesis the opposite

(6x2 − 5) + (-3x2 - x - 7)

combine like terms: 6x2 -3x2 and -5 -7 and -x

3x2 -x -12

and there you go. it's simplified :)

(6x2 - 5) - (3x2 + x + 7), execute the products (12-5) - (6+7 + x), execute the plus and minus operations 7 - (13 + x), take the parenthesis off 7 - 13 - x, execute the minus operation - 6 - x or, if the "x"s on 6x2 and 3x2 are variables execute the products (12x - 5) - (6x + x + 7), execute the plus operations and take the parenthesis off 12x - 5 - 7x - 7, execute the plus and minus operations 5x - 12

1.(12-5)+-(6+x+7)

2.7+-(13+x)

3.-6+x