To simplify the algebraic expression [tex]\( 15xy - 13 + 4x + 3y + xy + 21 \)[/tex], we need to combine like terms. Here’s a step-by-step breakdown:
1. Identify like terms:
- Terms with [tex]\( xy \)[/tex]: [tex]\( 15xy \)[/tex] and [tex]\( xy \)[/tex]
- Constant terms: [tex]\(-13\)[/tex] and [tex]\(21\)[/tex]
- Terms with [tex]\( x \)[/tex]: [tex]\(4x\)[/tex]
- Terms with [tex]\( y \)[/tex]: [tex]\(3y\)[/tex]
2. Combine like terms:
- Combine [tex]\( 15xy \)[/tex] and [tex]\( xy \)[/tex]:
[tex]\[
15xy + xy = 16xy
\][/tex]
- Combine the constants [tex]\(-13\)[/tex] and [tex]\(21\)[/tex]:
[tex]\[
-13 + 21 = 8
\][/tex]
- The terms [tex]\( 4x \)[/tex] and [tex]\( 3y \)[/tex] remain as they are since there are no other similar terms to combine.
3. Reassemble the expression:
- After combining like terms, the expression becomes:
[tex]\[
16xy + 4x + 3y + 8
\][/tex]
Thus, the simplified algebraic expression is [tex]\( 16xy + 4x + 3y + 8 \)[/tex].
Answer: C) [tex]\( 16xy + 4x + 3y + 8 \)[/tex]
