Question

Add the polynomial expressions 2r^2−3r+4 and −2r^2+3r+6
.

Answer 1

Add the expressions.

Expression 1: −3k+4k^3−2

Expression 2: 9k^2−3k^3+4k−3

Answer 2

Simplify (9x^2−6x+2) − (x^2+4x−39).

Answer 3

(1/4x^2−3x+2.25) + (0.75x^2+2x−14).

Answer 4

To add these two polynomial expressions, we need to add the coefficients of the like terms.

First, let's add the coefficients of the terms with the same degree:

2r^2 + (-2r^2) = 0r^2

Next, let's add the coefficients of the terms with the same degree:

-3r + 3r = 0r

Finally, let's add the constants:

4 + 6 = 10

Therefore, the sum of the polynomial expressions 2r^2−3r+4 and −2r^2+3r+6 is 0r^2 + 0r + 10, which can be simplified to 10.

Answer 5

To add the two expressions, let's combine like terms and arrange them in descending order of powers of k:

-3k + 4k^3 - 2 + 9k^2 - 3k^3 + 4k - 3

Rearranging the terms:

4k^3 - 3k^3 + 9k^2 - 3k - 3k + 4k - 2 - 3

Combining like terms:

(4k^3 - 3k^3) + 9k^2 + (4k - 3k - 3k) - 2 - 3

Simplifying:

k^3 + 9k^2 - 2k - 5

The sum of the two expressions is k^3 + 9k^2 - 2k - 5.

Answer 6

To simplify the expression (9x^2 - 6x + 2) - (x^2 + 4x - 39), distribute the negative sign to the second polynomial:

9x^2 - 6x + 2 - x^2 - 4x + 39

Combining like terms:

(9x^2 - x^2) + (-6x - 4x) + (2 + 39)

Simplifying further:

8x^2 - 10x + 41

Therefore, the simplified form of (9x^2 - 6x + 2) - (x^2 + 4x - 39) is 8x^2 - 10x + 41.

Answer 7

To add the expressions (1/4x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14), combine like terms:

(1/4x^2 + 0.75x^2) + (-3x + 2x) + (2.25 - 14)

Adding the terms:

(1/4 + 0.75)x^2 + (-3 + 2)x + (2.25 - 14)

Simplifying further:

(1.75)x^2 + (-x) + (-11.75)

Therefore, the sum of the expressions (1/4x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14) is 1.75x^2 - x - 11.75.