Simplify The Following Expression:${ (x-2)(x+1) } E X P R E S S I T I N T H E F O R M : Express It In The Form: E X P Ress I T In T H E F Or M : { x^2 + [?] X + \square \}

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Introduction

In this article, we will simplify the given expression $(x-2)(x+1)$ and express it in the form $x^2 + [?]x + \square$. This involves using the distributive property of multiplication over addition to expand the expression and then combining like terms.

The Distributive Property

The distributive property of multiplication over addition states that for any real numbers $a$, $b$, and $c$, the following equation holds:

$a(b+c) = ab + ac$

This property can be used to expand the given expression $(x-2)(x+1)$.

Expanding the Expression

Using the distributive property, we can expand the expression $(x-2)(x+1)$ as follows:

$(x-2)(x+1) = x(x+1) - 2(x+1)$

Now, we can use the distributive property again to expand each term:

$x(x+1) = x^2 + x$

$-2(x+1) = -2x - 2$

Therefore, the expanded expression is:

$x^2 + x - 2x - 2$

Combining Like Terms

Now, we can combine like terms in the expanded expression:

$x^2 + x - 2x - 2 = x^2 - x - 2$

Therefore, the simplified expression is:

$x^2 - x - 2$

Conclusion

In this article, we simplified the given expression $(x-2)(x+1)$ and expressed it in the form $x^2 + [?]x + \square$. We used the distributive property of multiplication over addition to expand the expression and then combined like terms to obtain the simplified expression $x^2 - x - 2$.

Key Takeaways

• The distributive property of multiplication over addition can be used to expand expressions.
• Like terms can be combined to simplify expressions.

Further Reading

For more information on simplifying expressions and using the distributive property, see the following resources:

• Algebraic Expressions
• Distributive Property

Example Problems

1. Simplify the expression $(x+3)(x-4)$.
2. Simplify the expression $(2x-1)(x+2)$.

Answer Key

1. $x^2 - x - 12$
2. $2x^2 + x - 2$

Discussion

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Introduction

In our previous article, we simplified the expression $(x-2)(x+1)$ and expressed it in the form $x^2 + [?]x + \square$. We used the distributive property of multiplication over addition to expand the expression and then combined like terms to obtain the simplified expression $x^2 - x - 2$. In this article, we will answer some frequently asked questions related to simplifying expressions and using the distributive property.

Q&A

Q: What is the distributive property of multiplication over addition?

A: The distributive property of multiplication over addition states that for any real numbers $a$, $b$, and $c$, the following equation holds:

$a(b+c) = ab + ac$

This property can be used to expand expressions and simplify them.

Q: How do I use the distributive property to simplify an expression?

A: To use the distributive property to simplify an expression, you need to follow these steps:

1. Expand the expression using the distributive property.
2. Combine like terms to simplify the expression.

For example, to simplify the expression $(x-2)(x+1)$, you would first expand it using the distributive property:

$(x-2)(x+1) = x(x+1) - 2(x+1)$

Then, you would combine like terms to simplify the expression:

$x(x+1) = x^2 + x$

$-2(x+1) = -2x - 2$

Therefore, the simplified expression is:

$x^2 + x - 2x - 2 = x^2 - x - 2$

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, $x$ and $-x$ are like terms because they both have the variable $x$ and the exponent $1$. Similarly, $x^2$ and $-x^2$ are like terms because they both have the variable $x$ and the exponent $2$.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, to combine the like terms $x$ and $-x$, you would add their coefficients:

$x + (-x) = 0$

Therefore, the combined term is $0$.

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

• Not using the distributive property to expand expressions.
• Not combining like terms to simplify expressions.
• Making errors when adding or subtracting coefficients.

Q: How can I practice simplifying expressions?

A: You can practice simplifying expressions by working on example problems and exercises. You can also use online resources and tools to help you practice and improve your skills.

Conclusion

In this article, we answered some frequently asked questions related to simplifying expressions and using the distributive property. We hope that this article has been helpful in clarifying any doubts you may have had about simplifying expressions. If you have any further questions or need additional help, please don't hesitate to ask.

Key Takeaways

• The distributive property of multiplication over addition can be used to expand expressions.
• Like terms can be combined to simplify expressions.
• Common mistakes to avoid when simplifying expressions include not using the distributive property, not combining like terms, and making errors when adding or subtracting coefficients.

Further Reading

For more information on simplifying expressions and using the distributive property, see the following resources:

• Algebraic Expressions
• Distributive Property

Example Problems

1. Simplify the expression $(x+3)(x-4)$.
2. Simplify the expression $(2x-1)(x+2)$.

Answer Key

1. $x^2 - x - 12$
2. $2x^2 + x - 2$

Discussion

What are some other ways to simplify expressions? How can the distributive property be used in real-world applications? Share your thoughts and ideas in the comments below!