Expanding and Simplifying (x+2)(x+5) to Standard Form
In mathematics, a polynomial is expressed in standard form when its terms are arranged in descending order of their exponents. The expression (x+2)(x+5) is in factored form and we can expand it to standard form using the distributive property.
Using the Distributive Property
The distributive property states that a(b + c) = ab + ac. We can apply this to our expression:

Distribute the first term: x(x + 5) + 2(x + 5)

Expand each term: x² + 5x + 2x + 10

Combine like terms: x² + 7x + 10
Therefore, (x+2)(x+5) in standard form is x² + 7x + 10.
Understanding the Result
The expanded form represents a quadratic equation, which is a polynomial with a highest degree of 2. This specific quadratic equation has:
 a coefficient of 1 for the x² term (x²),
 a coefficient of 7 for the x term (7x), and
 a constant term of 10 (10).
Understanding how to expand and simplify expressions like (x+2)(x+5) is crucial for solving quadratic equations, factoring polynomials, and working with other algebraic concepts.