Simplify The Expression:${ 7x^2 + 3 - 5(x^2 - 4) }$

Mar 12, 2025 by ADMIN 53 views

Simplify the Expression: $7x^2 + 3 - 5(x^2 - 4)$

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Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it is essential to understand the rules and techniques involved in simplifying expressions. In this article, we will simplify the given expression $7x^2 + 3 - 5(x^2 - 4)$ using the distributive property and combining like terms.

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. The distributive property can be written as:

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

This property can be applied to expressions with variables, constants, or a combination of both.

Applying the Distributive Property

To simplify the given expression, we will apply the distributive property to the term $-5(x^2 - 4)$ . This means we will multiply each term inside the parentheses with the term outside the parentheses, which is $-5$ .

$-5(x^2 - 4) = -5x^2 + 20$

Now, we can rewrite the original expression as:

$7x^2 + 3 - 5x^2 + 20$

Combining Like Terms

Like terms are terms that have the same variable raised to the same power. In this expression, we have two like terms: $7x^2$ and $-5x^2$ . We can combine these terms by adding their coefficients.

$7x^2 - 5x^2 = 2x^2$

Now, we can rewrite the expression as:

$2x^2 + 3 + 20$

Simplifying the Expression

We can simplify the expression further by combining the constant terms.

$3 + 20 = 23$

Now, we can rewrite the expression as:

$2x^2 + 23$

Conclusion

In this article, we simplified the expression $7x^2 + 3 - 5(x^2 - 4)$ using the distributive property and combining like terms. We applied the distributive property to expand the expression and then combined like terms to simplify it further. The final simplified expression is $2x^2 + 23$ .

Tips and Tricks

When simplifying expressions, it is essential to apply the distributive property to expand expressions with parentheses.
When combining like terms, make sure to add the coefficients of the like terms.
When simplifying expressions, always check for any common factors that can be factored out.

Frequently Asked Questions

Q: What is the distributive property? A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses.
Q: How do I apply the distributive property? A: To apply the distributive property, multiply each term inside the parentheses with the term outside the parentheses.
Q: How do I combine like terms? A: To combine like terms, add the coefficients of the like terms.

Final Answer

The final simplified expression is $2x^2 + 23$ .

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Introduction

In our previous article, we simplified the expression $7x^2 + 3 - 5(x^2 - 4)$ using the distributive property and combining like terms. In this article, we will answer some frequently asked questions related to simplifying expressions and provide additional tips and tricks to help you master this skill.

Q&A

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, multiply each term inside the parentheses with the term outside the parentheses. For example, if we have the expression $a(b + c)$ , we can apply the distributive property by multiplying $a$ with each term inside the parentheses: $ab + ac$ .

Q: How do I combine like terms?

A: To combine like terms, add the coefficients of the like terms. For example, if we have the expression $2x^2 + 3x^2$ , we can combine the like terms by adding the coefficients: $2 + 3 = 5$ , so the expression becomes $5x^2$ .

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2x^2$ and $3x^2$ are like terms because they both have the variable $x$ raised to the power of 2.

Q: How do I simplify expressions with fractions?

A: To simplify expressions with fractions, we can multiply the numerator and denominator by the same value to eliminate the fraction. For example, if we have the expression $\frac{2x^2}{3}$ , we can multiply the numerator and denominator by 3 to get rid of the fraction: $\frac{2x^2 \times 3}{3 \times 3} = \frac{6x^2}{9}$ .

Q: How do I simplify expressions with exponents?

A: To simplify expressions with exponents, we can use the rules of exponents to combine like terms. For example, if we have the expression $2^2 \times 2^3$ , we can combine the exponents by adding them: $2^2 \times 2^3 = 2^{2+3} = 2^5$ .

Tips and Tricks

When simplifying expressions, it is essential to apply the distributive property to expand expressions with parentheses.
When combining like terms, make sure to add the coefficients of the like terms.
When simplifying expressions, always check for any common factors that can be factored out.
When working with fractions, make sure to multiply the numerator and denominator by the same value to eliminate the fraction.
When working with exponents, make sure to use the rules of exponents to combine like terms.

Common Mistakes

Not applying the distributive property to expand expressions with parentheses.
Not combining like terms correctly.
Not checking for common factors that can be factored out.
Not multiplying the numerator and denominator by the same value to eliminate fractions.
Not using the rules of exponents to combine like terms.

Conclusion

Simplifying expressions is a crucial skill in mathematics, and it is essential to understand the rules and techniques involved in simplifying expressions. By applying the distributive property, combining like terms, and checking for common factors, you can simplify expressions with ease. Remember to always check your work and make sure to use the correct techniques to avoid common mistakes.

Final Answer

The final simplified expression is $2x^2 + 23$ .