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Add the polynomial expressions 2r2−3r+4

and −2r2+3r+6
.(1 point)

9 answers

To add the polynomial expressions \( 2r^2 - 3r + 4 \) and \( -2r^2 + 3r + 6 \), we will combine like terms.

  1. Combine the \( r^2 \) terms: \[ 2r^2 + (-2r^2) = 0r^2 \]

  2. Combine the \( r \) terms: \[ -3r + 3r = 0r \]

  3. Combine the constant terms: \[ 4 + 6 = 10 \]

Putting it all together, we have: \[ 0r^2 + 0r + 10 = 10 \]

Thus, the sum of the two polynomials is \( \boxed{10} \).

Add the expressions.

Expression 1: −3k+4k3−2


Expression 2: 9k2−3k3+4k−3


(2 points)

To add the expressions \( -3k + 4k^3 - 2 \) and \( 9k^2 - 3k^3 + 4k - 3 \), we'll combine like terms.

Expression 1:
\(-3k + 4k^3 - 2\)

Expression 2:
\(9k^2 - 3k^3 + 4k - 3\)

Now, let's arrange and group the like terms:

  1. Cubic Terms (\(k^3\)):
    \(4k^3 - 3k^3 = 1k^3\)

  2. Quadratic Terms (\(k^2\)):
    \(0k^2 + 9k^2 = 9k^2\)

  3. Linear Terms (\(k\)):
    \(-3k + 4k = 1k\)

  4. Constant Terms:
    \(-2 - 3 = -5\)

Putting all these together, we get the final result:

\[ 1k^3 + 9k^2 + 1k - 5 \]

Thus, the added expression can be written as:

\[ k^3 + 9k^2 + k - 5 \]

The final answer is \( \boxed{k^3 + 9k^2 + k - 5} \).

try again please

Let’s carefully add the two expressions step-by-step:

Given Expressions

Expression 1:
\(-3k + 4k^3 - 2\)

Expression 2:
\(9k^2 - 3k^3 + 4k - 3\)

Step 1: Write the expressions together

Combine both expressions:

\[ (-3k + 4k^3 - 2) + (9k^2 - 3k^3 + 4k - 3) \]

Step 2: Rearrange and group like terms

Now we can group all the \(k^3\), \(k^2\), \(k\), and constant terms:

\[ (4k^3 - 3k^3) + (9k^2) + (-3k + 4k) + (-2 - 3) \]

Step 3: Combine like terms

  1. Cubic Terms (\(k^3\)):
    \[ 4k^3 - 3k^3 = 1k^3 \]

  2. Quadratic Terms (\(k^2\)):
    \[ 0k^2 + 9k^2 = 9k^2 \]

  3. Linear Terms (\(k\)):
    \[ -3k + 4k = 1k \]

  4. Constant Terms:
    \[ -2 - 3 = -5 \]

Final Result

Putting it all together gives us:

\[ 1k^3 + 9k^2 + 1k - 5 \]

This can be written more simply as:

\[ k^3 + 9k^2 + k - 5 \]

Therefore, the final answer is \( \boxed{k^3 + 9k^2 + k - 5} \).

Simplify (9x2−6x+2)−(x2+4x−39)
.(1 point)
The difference of the polynomials is
.

To simplify the expression \( (9x^2 - 6x + 2) - (x^2 + 4x - 39) \), we will first distribute the negative sign across the second polynomial and then combine like terms.

Step 1: Distributing the negative sign

\[ (9x^2 - 6x + 2) - (x^2 + 4x - 39) = 9x^2 - 6x + 2 - x^2 - 4x + 39 \]

Step 2: Combine like terms

Now, we group the terms:

  1. Quadratic terms (\(x^2\)): \[ 9x^2 - x^2 = 8x^2 \]

  2. Linear terms (\(x\)): \[ -6x - 4x = -10x \]

  3. Constant terms: \[ 2 + 39 = 41 \]

Step 3: Write the simplified expression

Combining all of these, we get:

\[ 8x^2 - 10x + 41 \]

Thus, the difference of the polynomials is

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

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

To fill in the blanks, we need to set up the subtraction of the second polynomial from the first polynomial and also show the resulting difference.

Starting Polynomial Expressions

  1. First Polynomial (Expression 1):
    \( 9x^2 + x + 13 \)

  2. Second Polynomial (Expression 2):
    \( 2x^2 - 12x - (x^2 + 5x + 2) \)

Let's correctly set this up step-by-step:

Step 1: Formatting the Equation

To subtract the second polynomial, we rewrite it such that we switch the signs of the terms in the second polynomial:

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

This can also be rephrased as:

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

Step 2: Combine the Terms

Let's simplify this equation:

  1. Combine the second polynomial:

    \[ 2x^2 + 12x + 2 \]

Step 3: Writing the Final Polynomial

We can now set it up in blanks as requested:

  1. The first polynomial is \( 9x^2 \).
  2. The second polynomial is \( 2x^2 + 12x + 2 \).

Thus the entire setup will be:

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

Step 4: Calculation of the Resulting Difference

Now calculating the resulting differences:

  • Quadratic terms: \( 9x^2 - 2x^2 = 7x^2 \)
  • Linear terms: \( x - 12x = -11x \)
  • Constant terms: \( 13 - 2 = 11 \)

Thus the final expression becomes:

Final Result

The resulting polynomial expression is:

\[ 7x^2 - 11x + 11 \]

Filling in the Blanks

Given these details, here is how you might fill in the blanks:

  • First blank (first polynomial, \(9x^2\)): \(9x^2\)
  • Second blank (linear term, \(x\)): \(x\)
  • Third blank (constant term, \(13\)): \(13\)
  • Fourth blank (for \(12x\)): \(12x\)
  • Fifth blank (constant term, \(2\)): \(2\)

So the completed equation with blanks would be:

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

Resulting in the difference:

\[ = 7x^2 - 11x + 11 \]

If there are any adjustments needed based on the blanks provided in the original prompt, please let me know!