Rewrite Without Parentheses And Simplify.\[$(u + 3)^2\$\]

Feb 27, 2025 by ADMIN 58 views

**Expanding the Square of a Binomial Expression**

Introduction

In algebra, a binomial expression is a polynomial with two terms. When we square a binomial expression, we get a quadratic expression. In this article, we will focus on expanding the square of a binomial expression, specifically the expression $(u + 3)^2$ . We will use the formula for expanding a squared binomial and provide step-by-step examples to illustrate the process.

The Formula for Expanding a Squared Binomial

The formula for expanding a squared binomial is:

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

where $a$ and $b$ are any real numbers.

Applying the Formula to the Given Expression

Now, let's apply the formula to the given expression $(u + 3)^2$ . We can see that $a = u$ and $b = 3$ . Plugging these values into the formula, we get:

$(u + 3)^2 = u^2 + 2(u)(3) + 3^2$

Expanding the Expression

To expand the expression, we need to multiply the terms inside the parentheses. We can start by multiplying $u$ and $3$ :

$2(u)(3) = 6u$

Now, we can rewrite the expression as:

$(u + 3)^2 = u^2 + 6u + 3^2$

Simplifying the Expression

The final step is to simplify the expression by evaluating the exponent. In this case, we have $3^2 = 9$ . Therefore, the final expression is:

$(u + 3)^2 = u^2 + 6u + 9$

Conclusion

In this article, we have expanded the square of a binomial expression using the formula $(a + b)^2 = a^2 + 2ab + b^2$ . We have applied this formula to the expression $(u + 3)^2$ and simplified the resulting expression to get $u^2 + 6u + 9$ . This formula is a powerful tool for expanding squared binomials and can be used to simplify a wide range of algebraic expressions.

Examples and Applications

The formula for expanding a squared binomial has many practical applications in algebra and beyond. Here are a few examples:

Simplifying expressions: The formula can be used to simplify complex expressions by expanding the squared binomial and combining like terms.
Factoring expressions: The formula can be used to factor expressions by recognizing the pattern of a squared binomial.
Solving equations: The formula can be used to solve equations by expanding the squared binomial and setting it equal to zero.

Common Mistakes to Avoid

When expanding a squared binomial, there are several common mistakes to avoid:

Forgetting to multiply the terms: Make sure to multiply the terms inside the parentheses to get the correct expanded expression.
Forgetting to simplify the expression: Make sure to simplify the expression by evaluating the exponent and combining like terms.
Using the wrong formula: Make sure to use the correct formula for expanding a squared binomial, which is $(a + b)^2 = a^2 + 2ab + b^2$ .

Tips and Tricks

Here are a few tips and tricks for expanding squared binomials:

Use the formula as a template: Use the formula as a template to expand the squared binomial. Simply plug in the values of $a$ and $b$ and simplify the expression.
Check your work: Make sure to check your work by plugging the expanded expression back into the original equation.
Practice, practice, practice: The more you practice expanding squared binomials, the more comfortable you will become with the formula and the easier it will be to simplify complex expressions.

Conclusion

Introduction

In our previous article, we discussed how to expand the square of a binomial expression using the formula $(a + b)^2 = a^2 + 2ab + b^2$ . In this article, we will answer some common questions about expanding squared binomials and provide additional examples to help you practice this skill.

Q: What is the formula for expanding a squared binomial?

A: The formula for expanding a squared binomial is:

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

Q: How do I apply the formula to a given expression?

A: To apply the formula, simply plug in the values of $a$ and $b$ into the formula and simplify the expression. For example, if we want to expand the expression $(u + 3)^2$ , we can plug in $a = u$ and $b = 3$ into the formula:

$(u + 3)^2 = u^2 + 2(u)(3) + 3^2$

Q: What if I have a squared binomial with a negative term?

A: If you have a squared binomial with a negative term, you can simply apply the formula as usual. For example, if we want to expand the expression $(-u + 3)^2$ , we can plug in $a = -u$ and $b = 3$ into the formula:

$(-u + 3)^2 = (-u)^2 + 2(-u)(3) + 3^2$

Q: Can I use the formula to expand a squared binomial with a variable in the exponent?

A: No, the formula only works for squared binomials with a variable in the base, not in the exponent. For example, the expression $(u^2 + 3)^2$ cannot be expanded using the formula.

Q: How do I simplify the expression after expanding the squared binomial?

A: After expanding the squared binomial, you can simplify the expression by combining like terms and evaluating any exponents. For example, if we expand the expression $(u + 3)^2$ using the formula, we get:

$(u + 3)^2 = u^2 + 6u + 9$

We can simplify this expression by combining the like terms:

$(u + 3)^2 = u^2 + 6u + 9$

Q: Can I use the formula to expand a squared binomial with a fraction?

A: Yes, you can use the formula to expand a squared binomial with a fraction. For example, if we want to expand the expression $(\frac{u}{2} + 3)^2$ , we can plug in $a = \frac{u}{2}$ and $b = 3$ into the formula:

$(\frac{u}{2} + 3)^2 = (\frac{u}{2})^2 + 2(\frac{u}{2})(3) + 3^2$

Q: How do I check my work when expanding a squared binomial?

A: To check your work, you can plug the expanded expression back into the original equation and simplify. For example, if we expand the expression $(u + 3)^2$ using the formula, we get:

$(u + 3)^2 = u^2 + 6u + 9$

We can plug this expression back into the original equation:

$(u + 3)^2 = (u + 3)(u + 3)$

Expanding the right-hand side of the equation, we get:

$(u + 3)^2 = u^2 + 6u + 9$

This shows that our expanded expression is correct.

Conclusion

In this article, we have answered some common questions about expanding squared binomials and provided additional examples to help you practice this skill. Remember to always check your work by plugging the expanded expression back into the original equation. With practice, you will become proficient in expanding squared binomials and be able to simplify complex expressions with ease.