%5E2-in-standard-form.jpeg "(x+5)^2 In Standard Form")
Expanding (x + 5)² into Standard Form
The expression (x + 5)² represents the square of the binomial (x + 5). To express it in standard form, we need to expand it and simplify.
Understanding Standard Form
Standard form for a quadratic expression is ax² + bx + c, where 'a', 'b', and 'c' are constants.
Expanding the Expression
We can expand (x + 5)² using the distributive property (or FOIL method):
(x + 5)² = (x + 5)(x + 5)
- Multiply the first terms: x * x = x²
- Multiply the outer terms: x * 5 = 5x
- Multiply the inner terms: 5 * x = 5x
- Multiply the last terms: 5 * 5 = 25
Combining the terms, we get:
(x + 5)² = x² + 5x + 5x + 25
Simplifying the Expression
Combining the like terms, we obtain the standard form:
(x + 5)² = x² + 10x + 25
Conclusion
Therefore, the standard form of (x + 5)² is x² + 10x + 25. This expression represents a quadratic equation with a leading coefficient of 1, a linear coefficient of 10, and a constant term of 25.