To expand the expression [tex]\( x(x+2) + 1(x+2) \)[/tex], we will proceed step-by-step:
1. Distribute each term: Start by expanding the individual products within the expression.
[tex]\[
x(x+2) + 1(x+2)
\][/tex]
2. First distribute [tex]\( x \)[/tex] in the term [tex]\( x(x+2) \)[/tex]:
[tex]\[
x \cdot x + x \cdot 2 = x^2 + 2x
\][/tex]
3. Next distribute [tex]\( 1 \)[/tex] in the term [tex]\( 1(x+2) \)[/tex]:
[tex]\[
1 \cdot x + 1 \cdot 2 = x + 2
\][/tex]
4. Combine both expanded parts:
[tex]\[
x^2 + 2x + x + 2
\][/tex]
5. Simplify by combining like terms:
[tex]\[
x^2 + 2x + x + 2 = x^2 + 3x + 2
\][/tex]
Thus, the expanded form of [tex]\( x(x+2) + 1(x+2) \)[/tex] is:
[tex]\[
x^2 + 3x + 2
\][/tex]
Hence, the correct answer is not listed in the provided choices. The accurate expanded form is:
[tex]\[
\boxed{x^2 + 3x + 2}
\][/tex]
