When simplifying the expression (x^2 + 2x + 1), what does it factor to?

When simplifying the expression (x^2 + 2x + 1), what does it factor to?

• A. (x + 1)(x + 1)
• B. (x - 1)(x - 1)
• C. (x + 2)(x - 2)
• D. (x + 1)(x - 1)

Answer: (A)

To simplify the expression \(x^2 + 2x + 1\), we can look for a way to express it as the product of two binomials. The structure of the expression shows that we have a quadratic in standard form, where the coefficients correspond to a specific relationship. Notably, the expression can be recognized as a perfect square trinomial. The general form of a perfect square trinomial is \((a+b)^2 = a^2 + 2ab + b^2\). In this case, we can see that: - \(a\) is \(x\) (since \(x^2\) is the square of \(x\)), - \(b\) is \(1\) (since \(1^2 = 1\)). Applying the perfect square formula, we find: \[ x^2 + 2 \cdot x \cdot 1 + 1^2 = (x + 1)^2. \] Thus, the expression \(x^2 + 2x + 1\) factors to \((x + 1)(x + 1)\), or \((x + 1)^2\), confirming the choice

To simplify the expression (x^2 + 2x + 1), we can look for a way to express it as the product of two binomials. The structure of the expression shows that we have a quadratic in standard form, where the coefficients correspond to a specific relationship.

Notably, the expression can be recognized as a perfect square trinomial. The general form of a perfect square trinomial is ((a+b)^2 = a^2 + 2ab + b^2). In this case, we can see that:

• (a) is (x) (since (x^2) is the square of (x)),

• (b) is (1) (since (1^2 = 1)).

Applying the perfect square formula, we find:

[

x^2 + 2 \cdot x \cdot 1 + 1^2 = (x + 1)^2.

]

Thus, the expression (x^2 + 2x + 1) factors to ((x + 1)(x + 1)), or ((x + 1)^2), confirming the choice