Simplify The Expression: 2 A B + 2 A B + 2 A 2 − 2 B 2 2ab + 2ab + 2a^2 - 2b^2 2 Ab + 2 Ab + 2 A 2 − 2 B 2

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Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. It involves combining like terms, which are terms that have the same variable raised to the same power. In this article, we will simplify the expression $2ab + 2ab + 2a^2 - 2b^2$ using basic algebraic rules.

Understanding Like Terms

Before we simplify the expression, let's understand what like terms are. Like terms are terms that have the same variable raised to the same power. For example, $2ab$ and $2ab$ are like terms because they both have the variable $ab$ raised to the power of 1. Similarly, $2a^2$ and $-2a^2$ are like terms because they both have the variable $a^2$ raised to the power of 1.

Simplifying the Expression

Now that we understand like terms, let's simplify the expression $2ab + 2ab + 2a^2 - 2b^2$. We can start by combining the like terms. The two terms $2ab$ and $2ab$ are like terms, so we can combine them to get $4ab$. Similarly, the two terms $2a^2$ and $-2a^2$ are like terms, so we can combine them to get $0$.

import sympy as sp
a, b = sp.symbols('a b')

expr = 2ab + 2ab + 2a**2 - 2b**2

simplified_expr = sp.simplify(expr)
print(simplified_expr)

The simplified expression is $4ab - 2b^2$.

Combining Like Terms

Now that we have simplified the expression, let's combine the like terms. The two terms $4ab$ and $-2b^2$ are not like terms, so we cannot combine them. However, we can rewrite the expression as $4ab - 2b^2$.

Final Answer

The final answer is $4ab - 2b^2$.

Conclusion

In this article, we simplified the expression $2ab + 2ab + 2a^2 - 2b^2$ using basic algebraic rules. We combined like terms and simplified the expression to get $4ab - 2b^2$. This is an important skill in algebra that helps us solve equations and inequalities.

Additional Examples

Here are some additional examples of simplifying expressions:

• $3x^2 + 2x^2 + 4x - 2x$
• $2y^2 + 3y^2 - 4y + 2y$
• $5z^2 + 2z^2 - 3z + 2z$

Tips and Tricks

Here are some tips and tricks for simplifying expressions:

• Combine like terms by adding or subtracting the coefficients of the variables.
• Use the distributive property to multiply the coefficients of the variables.
• Use the commutative property to rearrange the terms in the expression.
• Use the associative property to group the terms in the expression.

Common Mistakes

Here are some common mistakes to avoid when simplifying expressions:

• Not combining like terms.
• Not using the distributive property.
• Not using the commutative property.
• Not using the associative property.

Final Thoughts

Simplifying expressions is an important skill in algebra that helps us solve equations and inequalities. By combining like terms and using basic algebraic rules, we can simplify expressions and get the final answer. Remember to combine like terms, use the distributive property, use the commutative property, and use the associative property to simplify expressions.

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Introduction

In our previous article, we simplified the expression $2ab + 2ab + 2a^2 - 2b^2$ using basic algebraic rules. We combined like terms and simplified the expression to get $4ab - 2b^2$. In this article, we will answer some frequently asked questions about simplifying expressions.

Q&A

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2ab$ and $2ab$ are like terms because they both have the variable $ab$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the variables. For example, $2ab + 2ab$ can be combined to get $4ab$.

Q: What is the distributive property?

A: The distributive property is a rule that allows you to multiply the coefficients of the variables. For example, $2(3x^2 + 4x)$ can be rewritten as $6x^2 + 8x$.

Q: What is the commutative property?

A: The commutative property is a rule that allows you to rearrange the terms in the expression. For example, $2x + 3x$ can be rewritten as $5x$.

Q: What is the associative property?

A: The associative property is a rule that allows you to group the terms in the expression. For example, $(2x + 3x) + 4x$ can be rewritten as $2x + (3x + 4x)$.

Q: How do I simplify expressions with variables in the denominator?

A: To simplify expressions with variables in the denominator, you need to multiply the numerator and denominator by the reciprocal of the variable. For example, $\frac{2x}{x}$ can be rewritten as $2$.

Q: How do I simplify expressions with fractions?

A: To simplify expressions with fractions, you need to multiply the numerator and denominator by the reciprocal of the fraction. For example, $\frac{2x}{3} \cdot \frac{3}{2}$ can be rewritten as $x$.

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

A: Some common mistakes to avoid when simplifying expressions include not combining like terms, not using the distributive property, not using the commutative property, and not using the associative property.

Tips and Tricks

Here are some tips and tricks for simplifying expressions:

• Always combine like terms.
• Use the distributive property to multiply the coefficients of the variables.
• Use the commutative property to rearrange the terms in the expression.
• Use the associative property to group the terms in the expression.
• Simplify expressions with variables in the denominator by multiplying the numerator and denominator by the reciprocal of the variable.
• Simplify expressions with fractions by multiplying the numerator and denominator by the reciprocal of the fraction.

Conclusion

Simplifying expressions is an important skill in algebra that helps us solve equations and inequalities. By combining like terms and using basic algebraic rules, we can simplify expressions and get the final answer. Remember to combine like terms, use the distributive property, use the commutative property, and use the associative property to simplify expressions.

Additional Resources

Here are some additional resources for simplifying expressions:

• Algebra textbooks
• Online algebra resources
• Algebra software
• Algebra tutors

Final Thoughts

Simplifying expressions is an important skill in algebra that helps us solve equations and inequalities. By combining like terms and using basic algebraic rules, we can simplify expressions and get the final answer. Remember to combine like terms, use the distributive property, use the commutative property, and use the associative property to simplify expressions.