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Understanding Equivalent Expressions with Variables and Exponents

In this lesson, you will learn how to read and write equivalent expressions using variables and exponents. This includes examples of simplifying expressions such as x + x + x and representing them in alternative forms like 3x or x + x + x + 4. We'll explore concepts of exponents, factors, and the significance of parentheses in structuring expressions. By the end of the lesson, you'll be able to create equivalent algebraic expressions for various examples and comprehend the fundamental principles of algebraic manipulation.

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Understanding Equivalent Expressions with Variables and Exponents

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  1. How do you read and write equivalent expressions using variables and exponents? For example, what equivalent expression could represent x + x + x?

  2. In this lesson you will learn how to read and write equivalent expressions by using variables and exponents.

  3. 15 ÷ y 4a-3 We know that algebraic expressions contain numbers, operations and at least one variable. 12 - w2 2(x + 3)

  4. Exponents show how many times the base number is used as a factor. exponent base 42 42 is equivalent to 4 • 4

  5. Parentheses can be used to show a part of an expression that needs to be done first. 5(x + 2) - 6

  6. Multiplying the base number by the exponent exponent base 42 42is not equivalent to 4 • 2 42≠ 4 • 2

  7. Let’s look at the expression x + x + x for x = 4. x + x + x 4 + 4 + 4 2x + x 2(4)+ 4 3x 3(4)

  8. Let’s write an equivalent algebraic expression for x times x plus 3. Since “x” is used as a factor two times, we can write x2. x • x + 3 So, an equivalent expression for x• x + 3 is x2 + 3. x2 + 3

  9. How could we write the algebraic expression for two times the quantity of x2 plus x? 2(x2 + x) is the same as (x2 + x) + (x2 + x) or x2 + x + x2 + x factor times 2

  10. In this lesson you have learned how to read and write equivalent expressions by using variables and exponents.

  11. Write two equivalent expressions for ten times the quantity of a number squared plus three.

  12. Write an equivalent expression for each of the following: • x + 1 + x • y + y + y + y • 2x2 • 3(y + 5)

  13. Write an equivalent expression for 2(a + 2). Write an equivalent expression for 2x2+ 5.

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