Haynes Santiago
08/06/2024 · Elementary School
\( \left. \begin{array} { l } { = x ^ { 3 } + 7 x ^ { 2 } + 8 x + 4 } \\ { + 3 x ^ { 3 } + 12 x ^ { 2 } + 5 x + 11 } \end{array} \right. \)
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Tutor-Verified Answer
Step-by-step Solution
To simplify the expression given, we need to combine the two polynomials:
\[
x^3 + 7x^2 + 8x + 4 + 3x^3 + 12x^2 + 5x + 11
\]
We can group the like terms together:
1. **Cubic terms**: \(x^3 + 3x^3 = 4x^3\)
2. **Quadratic terms**: \(7x^2 + 12x^2 = 19x^2\)
3. **Linear terms**: \(8x + 5x = 13x\)
4. **Constant terms**: \(4 + 11 = 15\)
Now, we can combine all these results:
\[
4x^3 + 19x^2 + 13x + 15
\]
Thus, the simplified expression is:
\[
\boxed{4x^3 + 19x^2 + 13x + 15}
\]
Quick Answer
The simplified expression is \(4x^3 + 19x^2 + 13x + 15\).
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