Subraction
(1/6x^3-1/10x-1/5)-(-1/6x^3+1/10x-1/5)
(1/6x^3-1/10x-1/5)-(-1/6x^3+1/10x-1/5)
= (1/6)x^3 - (1/10)x - 1/5 + (1/6)x^3 - (1/10)x + 1/5
= (1/3)x^3 - (1/5)x
or
x^3/3 - x/5
To subtract the expressions (1/6x^3 - 1/10x - 1/5) - (-1/6x^3 + 1/10x - 1/5), you will first need to distribute the negative sign to each term inside the parentheses.
(-1/6x^3 + 1/10x - 1/5) becomes -1/6x^3 * -1 + 1/10x * -1 + -1/5 * -1.
Using the distributive property of multiplication over addition, this simplifies to:
1/6x^3 - 1/10x + 1/5.
Now, subtract this from the original expression (1/6x^3 - 1/10x - 1/5).
This can be done by changing the subtraction into addition and changing the sign of each term in the parentheses:
(1/6x^3 - 1/10x - 1/5) + (-1/6x^3 + 1/10x - 1/5).
Now, combine like terms.
The x^3 terms cancel out (1/6x^3 - 1/6x^3 = 0).
The x terms cancel out (-1/10x + 1/10x = 0).
The constant terms add (-1/5 + -1/5 = -2/5).
Therefore, the final simplified result is -2/5.
To solve the subtraction problem
(1/6x^3 - 1/10x - 1/5) - (-1/6x^3 + 1/10x - 1/5),
we need to combine like terms.
First, let's distribute the negative sign to each term inside the parentheses of the second expression:
(1/6x^3 - 1/10x - 1/5) + 1/6x^3 - 1/10x + 1/5.
Now, let's group the like terms together:
(1/6x^3 + 1/6x^3) + (-1/10x - 1/10x) + (-1/5 + 1/5) - 1/5.
Simplifying each group of like terms:
2/6x^3 - 2/10x + 0 - 1/5.
Next, let's simplify the fractions:
1/3x^3 - 1/5x - 1/5.
Therefore, the simplified form of the subtraction expression is 1/3x^3 - 1/5x - 1/5.