Question

Use a vertical format or a horizontal format to add or subtract. $$\left(9 x^{3}+12\right)+\left(16 x^{3}-4 x+2\right)$$

Short answer

The simplified form of the given expression is \(25x^3 - 4x + 14\).

Step-by-step solution

Identify like terms

In both polynomials, like terms are terms that have the same variable raised to the same power. Here, the like terms are \(9x^3\) and \(16x^3\) because both have the variable \(x\) raised to the power of 3.

Combine like terms

Add the coefficients of the like terms together. So \(9x^3 + 16x^3\) become \(25x^3\). Since there are no like terms for \(-4x\) and \(2\), they are added directly to the result.

Present the final result

The polynomial, after combining like terms, is presented as \(25x^3 - 4x + 2 + 12\) or simplified to: \(25x^3 - 4x + 14\).