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(x+8)^2 As A Trinomial In Standard Form

2 min read Jun 17, 2024
(x+8)^2 As A Trinomial In Standard Form

Expanding (x + 8)^2 into a Trinomial

The expression (x + 8)^2 represents the square of a binomial, which can be expanded into a trinomial in standard form. Here's how we do it:

Understanding the Concept

Remember that squaring a binomial means multiplying it by itself. So, (x + 8)^2 is equivalent to (x + 8)(x + 8).

Using the FOIL Method

We can expand this product using the FOIL method:

  • First: x * x = x^2
  • Outer: x * 8 = 8x
  • Inner: 8 * x = 8x
  • Last: 8 * 8 = 64

Now, combine the like terms:

x^2 + 8x + 8x + 64 = x^2 + 16x + 64

Result

Therefore, the trinomial in standard form for (x + 8)^2 is x^2 + 16x + 64.

Key Points

  • This process is often referred to as squaring a binomial.
  • The result will always be a trinomial.
  • The coefficient of the middle term is twice the product of the terms in the original binomial.
  • The constant term is the square of the second term in the original binomial.

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