(x+5)^2 As A Trinomial In Standard Form

2 min read Jun 17, 2024

Expanding (x + 5)² to a Trinomial in Standard Form

In mathematics, a trinomial is a polynomial with three terms. To express the expression (x + 5)² as a trinomial in standard form, we need to expand it and arrange the terms in descending order of their exponents.

Understanding the Expression

(x + 5)² represents the square of the binomial (x + 5). This means we are multiplying the binomial by itself:

(x + 5)² = (x + 5)(x + 5)

Expanding the Expression

To expand the expression, we use the distributive property (also known as FOIL - First, Outer, Inner, Last):

Multiply the First terms: x * x = x²
Multiply the Outer terms: x * 5 = 5x
Multiply the Inner terms: 5 * x = 5x
Multiply the Last terms: 5 * 5 = 25

This gives us: x² + 5x + 5x + 25

Combining Like Terms

Now, we combine the like terms (the terms with the same variable and exponent):

x² + (5x + 5x) + 25

This simplifies to: x² + 10x + 25

Standard Form

The trinomial x² + 10x + 25 is now in standard form, arranged in descending order of their exponents.

Therefore, (x + 5)² expressed as a trinomial in standard form is x² + 10x + 25.