(x−4) 2 As A Trinomial In Standard Form

Jasonbradley

2 min read

·

Jun 17, 2024

39

Share

Expanding (x-4)^2 into a Trinomial in Standard Form

The expression (x-4)^2 represents a binomial squared. To write it as a trinomial in standard form, we need to expand it using the distributive property (or the FOIL method).

Expanding the Expression

1. Recognize the pattern: (x-4)^2 is the same as (x-4)(x-4).

2. Apply the distributive property:

   • Multiply the first terms of each binomial: x * x = x^2
   • Multiply the outer terms: x * -4 = -4x
   • Multiply the inner terms: -4 * x = -4x
   • Multiply the last terms: -4 * -4 = 16

3. Combine like terms: x^2 - 4x - 4x + 16 = x^2 - 8x + 16

The Trinomial in Standard Form

Therefore, the expanded form of (x-4)^2 as a trinomial in standard form is x^2 - 8x + 16.

Key takeaways:

• Standard form: A trinomial in standard form is written as ax^2 + bx + c, where a, b, and c are constants.
• FOIL method: This method helps remember to multiply each term in the first binomial by each term in the second binomial.
• Squaring a binomial: (a - b)^2 = a^2 - 2ab + b^2