Asked by adaleta

Simplify (9x2−6x+2)−(x2+4x−39)
.(1 point)
The difference of the polynomials is
Answered by adaleta
Fill in the blanks to complete the polynomial equation that shows the subtraction of the second expression from the first and the resulting difference. (2 points)
9x2
+
x + 13
– 2x2
+ 12x
+

x2
+ 5x
+ 2
Answered by adaleta
Simplify (14x2−3x+2.25)+(0.75x2+2x−14)
.(1 point)
The sum of the polynomials is
.
Answered by GPT-4o mini
To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), follow these steps:

1. Distribute the negative sign to the second polynomial:
\[
(9x^2 - 6x + 2) - (x^2 + 4x - 39) = 9x^2 - 6x + 2 - x^2 - 4x + 39
\]

2. Combine like terms:

- Combine \(9x^2\) and \(-x^2\):
\[
9x^2 - x^2 = 8x^2
\]

- Combine \(-6x\) and \(-4x\):
\[
-6x - 4x = -10x
\]

- Combine \(2\) and \(39\):
\[
2 + 39 = 41
\]

3. Putting it all together:
\[
8x^2 - 10x + 41
\]

Thus, the simplified difference of the polynomials is:
\[
\boxed{8x^2 - 10x + 41}
\]
Answered by GPT-4o mini
To fill in the blanks for the polynomial equation that shows the subtraction of the second expression from the first, we begin with:

\[
(9x^2 + \_\_ x + 13) - (2x^2 + 12x + \_\_ x^2 + 5x + 2)
\]

1. Let's define the first polynomial:
- The first polynomial is \(9x^2 + \_\_ x + 13\), where we'd typically put the coefficient of \(x\) which is required for our equation:
- Here, the coefficient of \(x\) is \(-10\) from the previous calculations.

So this can be rewritten as:
\[
(9x^2 - 10x + 13) - (2x^2 + 12x + \_\_ + 5x + 2)
\]

2. Now, observe the second polynomial \(2x^2 + 12x + \_\_ + 5x + 2\):
- We require to gather the coefficients accordingly considering we want to subtract the entirety and find the resulting difference.

This can be simplified as:
\[
2x^2 + (12x + 5x) + 2
\]
3. According to our previous result, we defined the remaining part as \(x^2\) + \(5x\) + \(2\), we can now deliver our outputs.

Thus, filling in the blanks, we have:

- First blank for the first polynomial: **\(-10\)** (for the coefficient of \(x\))
- Second blank for the second polynomial: **\(x^2\)** (reducing to \(x^2\))
- Third blank is **\(2\)** (from the originally defined polynomial)

So, the completed polynomial equation is:

\[
9x^2 - 10x + 13 - (2x^2 + 12x + x^2 + 5x + 2)
\]

This represents the subtraction clearly showing both polynomials and results respectively.
Answered by GPT-4o mini
To simplify the expression \((14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)\), we follow these steps:

1. Combine like terms:

- For the \(x^2\) terms:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]

- For the \(x\) terms:
\[
-3x + 2x = -1x \quad \text{or} \quad -x
\]

- For the constant terms:
\[
2.25 - 14 = 2.25 - 14 = -11.75
\]

2. Putting it all together:

The simplified polynomial is:
\[
14.75x^2 - x - 11.75
\]

Thus, the sum of the polynomials is:
\[
\boxed{14.75x^2 - x - 11.75}
\]