%5E2-as-a-trinomial-in-standard-form.jpeg "(x+9)^2 As A Trinomial In Standard Form")
Expanding (x + 9)^2 into a Trinomial in Standard Form
The expression (x + 9)^2 represents the square of a binomial. To express this in the standard form of a trinomial (ax^2 + bx + c), we can use the distributive property or a handy pattern:
1. Using the Distributive Property:
- Expand: (x + 9)^2 = (x + 9)(x + 9)
- FOIL: (x + 9)(x + 9) = xx + x9 + 9x + 99
- Simplify: x^2 + 9x + 9x + 81
- Combine like terms: x^2 + 18x + 81
2. Using the Pattern:
- Recognize the pattern: (a + b)^2 = a^2 + 2ab + b^2
- Apply the pattern: (x + 9)^2 = x^2 + 2(x)(9) + 9^2
- Simplify: x^2 + 18x + 81
**Therefore, the trinomial (x + 9)^2 in standard form is x^2 + 18x + 81. **
This expansion illustrates the key concept of squaring a binomial: the result is always a trinomial with the following characteristics:
- The first term is the square of the first term of the binomial.
- The second term is twice the product of the two terms of the binomial.
- The third term is the square of the second term of the binomial.