Question

How can you tell if a trinomial is the square of a binomial?

Answer 1

To determine if a trinomial is the square of a binomial, check if it follows the pattern of a perfect square trinomial. A perfect square trinomial can be expressed as the square of a binomial.

Step-by-step explanation:

To determine if a trinomial is the square of a binomial, you need to check if the trinomial follows the pattern of the perfect square trinomial. A perfect square trinomial can be written as the square of a binomial, where the first term of the binomial is the square root of the first term of the trinomial, and the second term of the binomial is twice the product of the square root of the first term and the square root of the third term of the trinomial. This can be represented as:

Trinomial: ax^2 + bx + c

Binomial: (√a)x + (√c)

If the trinomial matches this pattern, then it is the square of a binomial. For example, if we have the trinomial x^2 + 6x + 9, we can see that it follows the pattern mentioned above:

Trinomial: 1x^2 + 2(1)(3)x + 3^2

Binomial: (√1)x + (√3)

Here, (√1) is equal to 1 and (√3) is equal to 3, so the trinomial can be expressed as (x + 3)^2, which is the square of the binomial (x + 3).

Answer 2

The square of a binomial is always a trinomail since
(a+b)^2=a^2+2ab+b^2 and so if you can write your trinomial as a^2+2ab+b^2 or a^2-2ab+b^2, it will be the square of a binomial specifically (a+b)^2 and (a-b)^2 respectively