Add the polynomial expressions 2r^2−3r+4 and −2r^2+3r+6
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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.
Add the expressions.
Expression 1: −3k+4k^3−2
Expression 2: 9k^2−3k^3+4k−3
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.
Simplify (9x^2−6x+2) − (x^2+4x−39).
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.
(1/4x^2−3x+2.25) + (0.75x^2+2x−14).
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.