Question

Please elaborate

`Simplify (2x-7)(x+3)-(-3x^(2) -4)`

Answer 1

(2x-7)(x+3)-(-3x^[2] - 4)

====

5x^[2] -x -17

To begin simplifying this expression, we will foil the first half of it:

(2x-7)(x+3)

2x*x + 2x*3 - 7*x - 7*3

2x^[2] + 6x - 7x - 21

With this, we combine like terms:

2x^[2]-x-21

We now have

2x^[2]-x-21-(-3x^[2]-4)

We can now do the binomial distribution in the second half of the expression. Remember, the - sign in front of the parentheses means we are negating everything inside. In other words, we are multiplying -1 by everything inside the parentheses. Following this:

-(-3x^[2]-4) becomes

-1*-3x^[2] + -1*-4 = 3x^[2]+4

We have now simplified the first and second half of our expression, so we have:

2x^[2]-x-21+3x^[2]+4

And combining like terms we get

2x^[2]+3x^[2]-x-21+4 =

5x^[2] -x -17

We can use the quadratic expression to determine if the trinomial can be factored evenly, but it cannot so we have our final simplifed expression!

Answer 2

`5x^2 - x - 17`

Explanation:

Distribute the terms inside the first set of parentheses:

`(2x - 7)(x + 3) = 2x^2 + 6x - 7x - 21`

Combine like terms:

`= 2x^2 - x - 21`

Simplify by adding the second part:

`2x^2 - x - 21 - (-3x^2 - 4)`

Subtracting a negative is the same as adding the positive equivalent:

`= 2x^2 - x - 21 + 3x^2 + 4`

Combine like terms:

`= 5x^2 - x - 17`