Question

Use a horizontal format to add or subtract. $$\left(3 n^{3}+2 n-7\right)-\left(n^{3}-n-2\right)$$

Short answer

The simplified form of the given expression is \(2n^{3}+3n-5 \)

Step-by-step solution

Understand the problem and set up the equation

The problem is asking to subtract the expression \(n^{3}-n-2\) from the expression \(3n^{3}+2n-7\). This operation is similar to subtracting basic numbers. It can be set up as follows: \( (3n^{3}+2n-7) - (n^{3}-n-2) \)

Apply the distributive property

When we subtract an expression that is contained in brackets, the negative sign applies to every term inside the bracket. This is a part of the distributive property of multiplication over addition in mathematics, where the coefficient outside the bracket multiplies with each term inside the bracket individually. So, our expression will become: \(3n^{3}+2n-7-n^{3}+n+2 \)

Simple similar terms

Combining like terms (similar terms) involves adding or subtracting the coefficients of the like terms. In our case, \(3n^{3}-n^{3}\), \(2n+n\) and \(-7+2\) are like terms. Simplifying, we get \(2n^{3}+3n-5 \)