High School

Find the sum:

[tex]\[ 19x^3 + (14x + 4x^3) \][/tex]

A. [tex]\[ 37x^3 \][/tex]

B. [tex]\[ 37x^7 \][/tex]

C. [tex]\[ 22x^3 + 14x \][/tex]

D. [tex]\[ 23x^3 + 14x \][/tex]

Answer :

To find the sum of the expression [tex]\(19x^3 + (14x + 4x^3)\)[/tex], you need to combine like terms.

1. Identify and group like terms:
- First, look for terms involving [tex]\(x^3\)[/tex]. We have [tex]\(19x^3\)[/tex] and [tex]\(4x^3\)[/tex].
- For terms involving [tex]\(x\)[/tex], we have [tex]\(14x\)[/tex].

2. Add the like terms:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(19x^3 + 4x^3\)[/tex]. Add their coefficients: [tex]\(19 + 4 = 23\)[/tex]. So, the combined x³ term is [tex]\(23x^3\)[/tex].
- The term with [tex]\(x\)[/tex] remains the same as it stands alone: [tex]\(14x\)[/tex].

3. Write the simplified expression:
- After combining the terms, the resulting expression is [tex]\(23x^3 + 14x\)[/tex].

Therefore, the final simplified expression is [tex]\(23x^3 + 14x\)[/tex].

Looking at the options provided:
- A. [tex]\(37x^3\)[/tex]
- B. [tex]\(37x^7\)[/tex]
- C. [tex]\(22x^3 + 14x\)[/tex]
- D. [tex]\(23x^3 + 14x\)[/tex]

The correct answer is D. [tex]\(23x^3 + 14x\)[/tex].