Fiona Wrote Out The Description Of Each Step For Her Multiplication Of The Binomial And Trinomial \[$(2x - 3)(5x^2 - 2x + 7)\$\].Fiona's Product:$\[ \begin{tabular}{|l|l|l|} \hline & \multicolumn{1}{|c|}{Steps} & \multicolumn{1}{c|}{Result}

Introduction

Multiplication of binomial and trinomial is a fundamental concept in algebra that requires careful attention to detail and a clear understanding of the distributive property. In this article, we will guide you through the process of multiplying a binomial and a trinomial, step by step, using the example given by Fiona.

Understanding the Problem

Fiona has written out the description of each step for her multiplication of the binomial and trinomial $(2x - 3)(5x^2 - 2x + 7)$. To solve this problem, we need to follow the order of operations and apply the distributive property to each term.

Step 1: Multiply the First Term of the Binomial by Each Term of the Trinomial

To start, we multiply the first term of the binomial, $2x$, by each term of the trinomial, $5x^2$, $-2x$, and $7$. This gives us:

$2x \cdot 5x^2 = 10x^3$

$2x \cdot (-2x) = -4x^2$

$2x \cdot 7 = 14x$

Step 2: Multiply the Second Term of the Binomial by Each Term of the Trinomial

Next, we multiply the second term of the binomial, $-3$, by each term of the trinomial, $5x^2$, $-2x$, and $7$. This gives us:

$-3 \cdot 5x^2 = -15x^2$

$-3 \cdot (-2x) = 6x$

$-3 \cdot 7 = -21$

Step 3: Combine Like Terms

Now that we have multiplied each term of the binomial by each term of the trinomial, we need to combine like terms. This means adding or subtracting terms that have the same variable and exponent.

$10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21$

Combining like terms, we get:

$10x^3 - 19x^2 + 20x - 21$

Fiona's Product

Fiona's product is the result of multiplying the binomial and trinomial:

$(2x - 3)(5x^2 - 2x + 7) = 10x^3 - 19x^2 + 20x - 21$

Conclusion

Multiplication of binomial and trinomial requires careful attention to detail and a clear understanding of the distributive property. By following the order of operations and applying the distributive property to each term, we can solve this problem step by step. Fiona's product is the result of multiplying the binomial and trinomial, and it is an important concept in algebra.

Tips and Tricks

• Make sure to follow the order of operations and apply the distributive property to each term.
• Combine like terms carefully to avoid errors.
• Use a table or chart to help organize the multiplication process.

Common Mistakes

• Failing to follow the order of operations.
• Not applying the distributive property to each term.
• Not combining like terms carefully.

Real-World Applications

Multiplication of binomial and trinomial has many real-world applications, including:

• Algebraic expressions in physics and engineering.
• Calculus and differential equations.
• Computer science and programming.

Conclusion

Introduction

In our previous article, we guided you through the process of multiplying a binomial and a trinomial, step by step, using the example given by Fiona. In this article, we will answer some of the most frequently asked questions about multiplication of binomial and trinomial.

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that states that a single term can be multiplied by each term in a polynomial. In other words, it allows us to multiply a single term by each term in a polynomial, rather than multiplying the entire polynomial by itself.

Q: How do I apply the distributive property to each term?

A: To apply the distributive property to each term, you need to multiply the single term by each term in the polynomial, one at a time. For example, if you have the expression $(2x - 3)(5x^2 - 2x + 7)$, you would multiply the single term $2x$ by each term in the polynomial, and then multiply the single term $-3$ by each term in the polynomial.

Q: What is the difference between a binomial and a trinomial?

A: A binomial is a polynomial with two terms, while a trinomial is a polynomial with three terms. In the example given by Fiona, the binomial is $(2x - 3)$ and the trinomial is $(5x^2 - 2x + 7)$.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract terms that have the same variable and exponent. For example, if you have the expression $10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21$, you would combine the like terms $-4x^2$ and $-15x^2$ to get $-19x^2$.

Q: What are some common mistakes to avoid when multiplying binomials and trinomials?

A: Some common mistakes to avoid when multiplying binomials and trinomials include:

• Failing to follow the order of operations.
• Not applying the distributive property to each term.
• Not combining like terms carefully.
• Not checking for errors in the multiplication process.

Q: How do I check my work when multiplying binomials and trinomials?

A: To check your work when multiplying binomials and trinomials, you can use the following steps:

• Multiply the binomial and trinomial using the distributive property.
• Combine like terms.
• Check that the final answer is correct by plugging it back into the original equation.

Q: What are some real-world applications of multiplication of binomials and trinomials?

A: Some real-world applications of multiplication of binomials and trinomials include:

• Algebraic expressions in physics and engineering.
• Calculus and differential equations.
• Computer science and programming.

Conclusion

In conclusion, multiplication of binomial and trinomial is an important concept in algebra that requires careful attention to detail and a clear understanding of the distributive property. By following the order of operations and applying the distributive property to each term, we can solve this problem step by step. We hope that this Q&A article has helped to clarify any questions you may have had about multiplication of binomial and trinomial.