Expand The Brackets: 5t (t² + 2t – 3)

Mar 9, 2025 by ADMIN 38 views

Expanding the Brackets: 5t (t² + 2t – 3)

Expanding brackets is a fundamental concept in algebra, and it's essential to understand how to do it correctly. In this article, we will focus on expanding the brackets of the given expression: 5t (t² + 2t – 3). We will break down the process step by step, and by the end of this article, you will be able to expand brackets with ease.

What are Brackets?

Brackets are used to group numbers, variables, or expressions together. They are essential in algebra as they help us to simplify complex expressions and solve equations. In the given expression, 5t (t² + 2t – 3), the brackets are used to group the terms inside them.

The Distributive Law

To expand the brackets, we will use the distributive law, which states that:

a(b + c) = ab + ac

In the given expression, we can see that 5t is being multiplied by (t² + 2t – 3). We can use the distributive law to expand the brackets.

Step 1: Multiply 5t by t²

Using the distributive law, we can multiply 5t by t² as follows:

5t(t²) = 5t³

Step 2: Multiply 5t by 2t

Next, we will multiply 5t by 2t:

5t(2t) = 10t²

Step 3: Multiply 5t by -3

Finally, we will multiply 5t by -3:

5t(-3) = -15t

Expanding the Brackets

Now that we have multiplied 5t by each term inside the brackets, we can combine the results to get the expanded expression:

5t(t² + 2t – 3) = 5t³ + 10t² - 15t

Expanding brackets is a straightforward process that involves using the distributive law. By following the steps outlined in this article, you should be able to expand brackets with ease. Remember to multiply each term inside the brackets by the factor outside the brackets and then combine the results.

Tips and Tricks

Make sure to use the distributive law when expanding brackets.
Multiply each term inside the brackets by the factor outside the brackets.
Combine the results to get the expanded expression.
Practice expanding brackets with different expressions to become more confident.

Common Mistakes

Failing to use the distributive law when expanding brackets.
Not multiplying each term inside the brackets by the factor outside the brackets.
Not combining the results to get the expanded expression.

Real-World Applications

Expanding brackets has many real-world applications, including:

Simplifying complex expressions in algebra.
Solving equations in physics and engineering.
Modeling real-world situations in economics and finance.

Example Problems

Expand the brackets: 2x (x² + 3x – 4)
Expand the brackets: 3y (y² – 2y + 1)
Expand the brackets: 4z (z² + 5z – 2)

Solutions

2x (x² + 3x – 4) = 2x³ + 6x² - 8x
3y (y² – 2y + 1) = 3y³ - 6y² + 3y
4z (z² + 5z – 2) = 4z³ + 20z² - 8z
Expanding the Brackets: 5t (t² + 2t – 3) - Q&A

In our previous article, we discussed how to expand the brackets of the given expression: 5t (t² + 2t – 3). We broke down the process step by step and provided examples to help you understand the concept. In this article, we will answer some frequently asked questions related to expanding brackets.

Q: What is the distributive law?

A: The distributive law is a fundamental concept in algebra that states that:

a(b + c) = ab + ac

This law allows us to expand brackets by multiplying each term inside the brackets by the factor outside the brackets.

Q: How do I expand brackets with multiple terms?

A: To expand brackets with multiple terms, you can use the distributive law to multiply each term inside the brackets by the factor outside the brackets. For example, if you have the expression 2x (x² + 3x – 4), you can expand it as follows:

2x (x² + 3x – 4) = 2x³ + 6x² - 8x

Q: What if I have a negative sign outside the brackets?

A: If you have a negative sign outside the brackets, you can simply multiply each term inside the brackets by the negative sign. For example, if you have the expression -3y (y² – 2y + 1), you can expand it as follows:

-3y (y² – 2y + 1) = -3y³ + 6y² - 3y

Q: Can I expand brackets with variables and constants?

A: Yes, you can expand brackets with variables and constants. For example, if you have the expression 4z (z² + 5z – 2), you can expand it as follows:

4z (z² + 5z – 2) = 4z³ + 20z² - 8z

Q: What if I have a fraction outside the brackets?

A: If you have a fraction outside the brackets, you can simply multiply each term inside the brackets by the fraction. For example, if you have the expression 1/2x (x² + 3x – 4), you can expand it as follows:

1/2x (x² + 3x – 4) = 1/2x³ + 3/2x² - 2x

Q: Can I expand brackets with exponents?

A: Yes, you can expand brackets with exponents. For example, if you have the expression 2x² (x³ + 3x² – 4), you can expand it as follows:

2x² (x³ + 3x² – 4) = 2x⁵ + 6x⁴ - 8x²

Q: What if I have a binomial outside the brackets?

A: If you have a binomial outside the brackets, you can use the distributive law to expand it. For example, if you have the expression (x + 2) (x² + 3x – 4), you can expand it as follows:

(x + 2) (x² + 3x – 4) = x³ + 3x² - 4x + 2x² + 6x - 8

Q: Can I expand brackets with radicals?

A: Yes, you can expand brackets with radicals. For example, if you have the expression 2√x (x² + 3x – 4), you can expand it as follows:

2√x (x² + 3x – 4) = 2√x³ + 6√x² - 8√x

Expanding brackets is a fundamental concept in algebra that has many real-world applications. By understanding how to expand brackets, you can simplify complex expressions and solve equations. In this article, we answered some frequently asked questions related to expanding brackets. We hope that this article has helped you to better understand the concept of expanding brackets.