Sure! Let's expand and simplify the expression [tex]\((x+2)(x+1)\)[/tex] step by step.
1. Apply the distributive property:
To expand [tex]\((x+2)(x+1)\)[/tex], we need to use the distributive property of multiplication over addition. This means multiplying each term in the first binomial by each term in the second binomial.
[tex]\[
(x + 2)(x + 1) = x \cdot (x + 1) + 2 \cdot (x + 1)
\][/tex]
2. Distribute each term:
- Distribute [tex]\(x\)[/tex] to both terms inside the parentheses:
[tex]\[
x \cdot (x + 1) = x \cdot x + x \cdot 1 = x^2 + x
\][/tex]
- Distribute [tex]\(2\)[/tex] to both terms inside the parentheses:
[tex]\[
2 \cdot (x + 1) = 2 \cdot x + 2 \cdot 1 = 2x + 2
\][/tex]
3. Combine the results:
Now, combine all the terms obtained from the distribution:
[tex]\[
x^2 + x + 2x + 2
\][/tex]
4. Combine like terms:
Finally, combine the like terms (terms with the same variable raised to the same power):
[tex]\[
x^2 + x + 2x + 2 = x^2 + (x + 2x) + 2 = x^2 + 3x + 2
\][/tex]
So, the expanded and simplified form of [tex]\((x+2)(x+1)\)[/tex] is:
[tex]\[
\boxed{x^2 + 3x + 2}
\][/tex]
