(x+4)^2 As A Trinomial In Standard Form

Jasonbradley

2 min read

·

Jun 16, 2024

39

Share

Expanding (x+4)² into a Trinomial

The expression (x+4)² represents the square of a binomial, which can be expanded into a trinomial in standard form. Here's how to do it:

Understanding the Process

The expression (x+4)² is equivalent to multiplying the binomial (x+4) by itself:

(x+4)² = (x+4)(x+4)

To expand this, we can use the FOIL method (First, Outer, Inner, Last):

1. First: Multiply the first terms of each binomial: x * x = x²
2. Outer: Multiply the outer terms of each binomial: x * 4 = 4x
3. Inner: Multiply the inner terms of each binomial: 4 * x = 4x
4. Last: Multiply the last terms of each binomial: 4 * 4 = 16

Now we combine the terms:

x² + 4x + 4x + 16

Finally, we combine the like terms:

x² + 8x + 16

Standard Form

The trinomial x² + 8x + 16 is in standard form, where the terms are arranged in descending order of their exponents.

This process can be generalized for any binomial squared:

(a + b)² = a² + 2ab + b²

Remember that the middle term of the trinomial is always twice the product of the two terms in the binomial.