70. Simplify: $0.2(k+8)-0.1k$71. Simplify: $10-3(2x+3y$\]72. Simplify: $14-11(5m+3n$\]73. Simplify: $6(3x-6)-2(x+1)-17x$74. Simplify: $7(2x+5)-4(x+2)-20x$75. Simplify: $\frac{1}{2}(12x-4)-(x+5$\]76.
Introduction
Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will explore the process of simplifying algebraic expressions, focusing on the rules and techniques used to combine like terms, eliminate parentheses, and reduce complex expressions to their simplest form.
Simplifying Expressions with Parentheses
70. Simplify:
To simplify this expression, we need to apply the distributive property, which states that for any real numbers a, b, and c, a(b + c) = ab + ac. In this case, we can rewrite the expression as:
Now, we can combine like terms by adding or subtracting the coefficients of the same variable:
Therefore, the simplified expression is .
71. Simplify:
To simplify this expression, we need to apply the distributive property again:
Now, we can combine like terms by adding or subtracting the coefficients of the same variable:
Therefore, the simplified expression is .
72. Simplify:
To simplify this expression, we need to apply the distributive property again:
Now, we can combine like terms by adding or subtracting the coefficients of the same variable:
Therefore, the simplified expression is .
Simplifying Expressions with Multiple Terms
73. Simplify:
To simplify this expression, we need to apply the distributive property and combine like terms:
Now, we can combine like terms by adding or subtracting the coefficients of the same variable:
Therefore, the simplified expression is .
74. Simplify:
To simplify this expression, we need to apply the distributive property and combine like terms:
Now, we can combine like terms by adding or subtracting the coefficients of the same variable:
Therefore, the simplified expression is .
Simplifying Expressions with Fractions
75. Simplify:
To simplify this expression, we need to apply the distributive property and combine like terms:
Now, we can combine like terms by adding or subtracting the coefficients of the same variable:
Therefore, the simplified expression is .
Conclusion
Q&A: Simplifying Algebraic Expressions
Q: What is the distributive property, and how is it used in simplifying algebraic expressions? A: The distributive property is a fundamental concept in algebra that states that for any real numbers a, b, and c, a(b + c) = ab + ac. It is used to simplify algebraic expressions by distributing the coefficients to the terms inside the parentheses.
Q: How do I combine like terms in an algebraic expression? A: To combine like terms, you need to add or subtract the coefficients of the same variable. For example, in the expression 2x + 3x, you can combine the like terms by adding the coefficients: 2x + 3x = 5x.
Q: What is the difference between a variable and a constant in an algebraic expression? A: A variable is a letter or symbol that represents a value that can change, while a constant is a value that remains the same. For example, in the expression 2x + 3, x is a variable and 3 is a constant.
Q: How do I simplify an algebraic expression with multiple terms? A: To simplify an algebraic expression with multiple terms, you need to apply the distributive property and combine like terms. For example, in the expression 2x + 3x - 4x, you can combine the like terms by adding or subtracting the coefficients: 2x + 3x - 4x = x.
Q: What is the order of operations in simplifying algebraic expressions? A: The order of operations in simplifying algebraic expressions is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I simplify an algebraic expression with fractions? A: To simplify an algebraic expression with fractions, you need to apply the distributive property and combine like terms. For example, in the expression 1/2(2x - 4) - x, you can simplify the expression by distributing the fraction to the terms inside the parentheses: 1/2(2x - 4) - x = x - 2 - x = -2.
Q: What are some common mistakes to avoid when simplifying algebraic expressions? A: Some common mistakes to avoid when simplifying algebraic expressions include:
- Not applying the distributive property correctly
- Not combining like terms correctly
- Not following the order of operations
- Not simplifying fractions correctly
Q: How can I practice simplifying algebraic expressions? A: You can practice simplifying algebraic expressions by working through exercises and problems in a textbook or online resource. You can also try simplifying expressions on your own and then checking your work with a calculator or by asking a teacher or tutor for help.
Conclusion
Simplifying algebraic expressions is an essential skill for students and professionals alike. By understanding the rules and techniques used to combine like terms, eliminate parentheses, and reduce complex expressions to their simplest form, you can make mathematical problems more manageable and easier to solve. In this article, we have explored the process of simplifying algebraic expressions, focusing on the rules and techniques used to combine like terms, eliminate parentheses, and reduce complex expressions to their simplest form. With practice and patience, anyone can master the art of simplifying algebraic expressions and become proficient in mathematical problem-solving.