Not identifying the binomial

Oct 13, 2025 by magicalceylontours.com 106 views

Introduction

In algebra, a perfect-square trinomial is a quadratic expression that can be factored into the square of a binomial. It has a specific form, which is $(a+b)^2 = a^2 + 2ab + b^2$ . In this article, we will explore how to identify and create perfect-square trinomials, with a focus on adding a value to the expression $x^2 + 16x$ to make it a perfect-square trinomial.

Understanding Perfect-Square Trinomials

A perfect-square trinomial is a quadratic expression that can be factored into the square of a binomial. The general form of a perfect-square trinomial is $(a+b)^2 = a^2 + 2ab + b^2$ . To identify a perfect-square trinomial, we need to look for the following characteristics:

The expression must be a quadratic expression, meaning it must have a degree of 2.
The expression must have the form $a^2 + 2ab + b^2$ .
The expression must be able to be factored into the square of a binomial.

Creating Perfect-Square Trinomials

To create a perfect-square trinomial, we need to follow these steps:

Identify the binomial: We need to identify the binomial that we want to square. This binomial will have the form $a+b$ .
Square the binomial: We need to square the binomial to get the perfect-square trinomial. This can be done using the formula $(a+b)^2 = a^2 + 2ab + b^2$ .
Expand the expression: We need to expand the expression to get the perfect-square trinomial.

Adding a Value to the Expression $x^2 + 16x$

Now, let's focus on adding a value to the expression $x^2 + 16x$ to make it a perfect-square trinomial. To do this, we need to follow these steps:

Identify the binomial: We need to identify the binomial that we want to square. In this case, the binomial is $x+8$ .
Square the binomial: We need to square the binomial to get the perfect-square trinomial. This can be done using the formula $(a+b)^2 = a^2 + 2ab + b^2$ .
Expand the expression: We need to expand the expression to get the perfect-square trinomial.

The Perfect-Square Trinomial

Using the formula $(a+b)^2 = a^2 + 2ab + b^2$ , we can square the binomial $x+8$ to get the perfect-square trinomial:

(x+8)^2 = x^2 + 2x(8) + 8^2

Expanding the expression, we get:

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

Conclusion

In conclusion, to make the expression $x^2 + 16x$ a perfect-square trinomial, we need to add 64 to the expression. This is because the perfect-square trinomial is $(x+8)^2 = x^2 + 16x + 64$ . Therefore, the correct answer is C. 64.

Final Answer

Q&A: Perfect-Square Trinomials

Q: What is a perfect-square trinomial?

A: A perfect-square trinomial is a quadratic expression that can be factored into the square of a binomial. It has a specific form, which is $(a+b)^2 = a^2 + 2ab + b^2$ .

Q: How do I identify a perfect-square trinomial?

A: To identify a perfect-square trinomial, you need to look for the following characteristics:

The expression must be a quadratic expression, meaning it must have a degree of 2.
The expression must have the form $a^2 + 2ab + b^2$ .
The expression must be able to be factored into the square of a binomial.

Q: How do I create a perfect-square trinomial?

A: To create a perfect-square trinomial, you need to follow these steps:

Identify the binomial: You need to identify the binomial that you want to square. This binomial will have the form $a+b$ .
Square the binomial: You need to square the binomial to get the perfect-square trinomial. This can be done using the formula $(a+b)^2 = a^2 + 2ab + b^2$ .
Expand the expression: You need to expand the expression to get the perfect-square trinomial.

Q: How do I add a value to the expression $x^2 + 16x$ to make it a perfect-square trinomial?

A: To add a value to the expression $x^2 + 16x$ to make it a perfect-square trinomial, you need to follow these steps:

Identify the binomial: You need to identify the binomial that you want to square. In this case, the binomial is $x+8$ .
Square the binomial: You need to square the binomial to get the perfect-square trinomial. This can be done using the formula $(a+b)^2 = a^2 + 2ab + b^2$ .
Expand the expression: You need to expand the expression to get the perfect-square trinomial.

Q: What is the perfect-square trinomial for the expression $x^2 + 16x$ ?

A: The perfect-square trinomial for the expression $x^2 + 16x$ is $(x+8)^2 = x^2 + 16x + 64$ .

Q: What value do I need to add to the expression $x^2 + 16x$ to make it a perfect-square trinomial?

A: To make the expression $x^2 + 16x$ a perfect-square trinomial, you need to add 64 to the expression.

Q: What is the final answer?

A: The final answer is C. 64.

Common Mistakes to Avoid

Not identifying the binomial: Make sure to identify the binomial that you want to square.
Not squaring the binomial: Make sure to square the binomial to get the perfect-square trinomial.
Not expanding the expression: Make sure to expand the expression to get the perfect-square trinomial.

Conclusion

In conclusion, perfect-square trinomials are a key concept in algebra that can be used to factor quadratic expressions. By following the steps outlined in this article, you can create perfect-square trinomials and add values to expressions to make them perfect-square trinomials. Remember to identify the binomial, square the binomial, and expand the expression to get the perfect-square trinomial.