(x+12)^2 As A Trinomial In Standard Form

2 min read Jun 16, 2024
(x+12)^2 As A Trinomial In Standard Form

Expanding (x + 12)^2 into a Trinomial

The expression (x + 12)^2 represents the square of a binomial. To express this in standard trinomial form, we need to expand it using the distributive property or by recognizing a pattern.

Using the Distributive Property

We can expand (x + 12)^2 by multiplying it by itself:

(x + 12)^2 = (x + 12)(x + 12)

Now, we can use the distributive property (also known as FOIL) to multiply the terms:

  • First: x * x = x^2
  • Outer: x * 12 = 12x
  • Inner: 12 * x = 12x
  • Last: 12 * 12 = 144

Combining like terms, we get:

x^2 + 12x + 12x + 144 = x^2 + 24x + 144

Using the Pattern

We can also recognize that squaring a binomial follows a specific pattern:

(a + b)^2 = a^2 + 2ab + b^2

In our case, a = x and b = 12. Applying the pattern, we get:

x^2 + 2(x)(12) + 12^2 = x^2 + 24x + 144

Conclusion

Both methods lead us to the same result: (x + 12)^2 expanded in standard trinomial form is x^2 + 24x + 144. This form is useful for simplifying expressions, solving equations, and understanding the relationship between different algebraic forms.

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