%5E2.jpeg "(a+1)^2")
Understanding (a + 1)²
The expression (a + 1)² is a common algebraic expression that often appears in various mathematical contexts. It represents the square of the binomial (a + 1), meaning it's multiplied by itself.
Expanding the Expression
To understand the meaning of (a + 1)², we can expand it using the distributive property:
(a + 1)² = (a + 1) * (a + 1)
Expanding the product, we get:
(a + 1) * (a + 1) = a * (a + 1) + 1 * (a + 1)
Applying the distributive property again:
= a² + a + a + 1
Combining like terms:
= a² + 2a + 1
Therefore, the expanded form of (a + 1)² is a² + 2a + 1.
Key Points
- Square of a binomial: (a + 1)² is a perfect square trinomial, representing the square of a binomial.
- Expansion: Expanding the expression yields a² + 2a + 1.
- Application: This expression is commonly used in algebra, calculus, and other mathematical fields.
Example:
Let's say a = 3. We can substitute this value into the expanded form of (a + 1)²:
(a + 1)² = a² + 2a + 1 (3 + 1)² = 3² + 2 * 3 + 1 4² = 9 + 6 + 1 16 = 16
As you can see, the equation holds true.
Conclusion
Understanding (a + 1)² and its expanded form is crucial for working with algebraic expressions. By applying the distributive property and simplifying, we can easily expand the expression and understand its value for various values of 'a'.