Simplify (9x2−6x+2)−(x2+4x−39)

Question

.(1 point)
The difference of the polynomials is

Answer 1

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: \[ \boxed{8x^2 - 10x + 41} \]

Answer 2

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

Answer 3

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.

Answer 4

Simplify (14x2−3x+2.25)+(0.75x2+2x−14)
.(1 point)
The sum of the polynomials is
.

Answer 5

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: \[ \boxed{14.75x^2 - x - 11.75} \]