To simplify the expression [tex]\(13x^2 - 12y + 8z + 8x^2 - 2z - 2y + 6x - z\)[/tex], we need to combine like terms. Follow these steps:
1. Identify and group like terms:
- The terms with [tex]\(x^2\)[/tex] are: [tex]\(13x^2\)[/tex] and [tex]\(8x^2\)[/tex].
- The terms with [tex]\(y\)[/tex] are: [tex]\(-12y\)[/tex] and [tex]\(-2y\)[/tex].
- The terms with [tex]\(z\)[/tex] are: [tex]\(8z\)[/tex], [tex]\(-2z\)[/tex], and [tex]\(-z\)[/tex].
- The term with [tex]\(x\)[/tex] is: [tex]\(6x\)[/tex].
2. Combine the like terms:
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(13x^2 + 8x^2\)[/tex]. This equals [tex]\(21x^2\)[/tex].
- Combine the [tex]\(y\)[/tex] terms: [tex]\(-12y - 2y\)[/tex]. This equals [tex]\(-14y\)[/tex].
- Combine the [tex]\(z\)[/tex] terms: [tex]\(8z - 2z - z\)[/tex]. This equals [tex]\(5z\)[/tex].
- We only have one [tex]\(x\)[/tex] term: [tex]\(6x\)[/tex].
3. Combine all the simplified terms together:
- The simplified expression becomes [tex]\(21x^2 - 14y + 5z + 6x\)[/tex].
Therefore, the simplified expression is:
[tex]\[ 21x^2 - 14y + 5z + 6x \][/tex]
