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Questions and Answers
What is the simplified form of 5x + 8 - 2x + 5?
What is the simplified form of 5x + 8 - 2x + 5?
What does the distributive property allow you to do with an expression like 9(5x + 4)?
What does the distributive property allow you to do with an expression like 9(5x + 4)?
How do you simplify the expression 5(3x + 4) - 7x + 8?
How do you simplify the expression 5(3x + 4) - 7x + 8?
What is the product of the monomials 4x³ and 5x²?
What is the product of the monomials 4x³ and 5x²?
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What is the result of dividing x⁸ by x³?
What is the result of dividing x⁸ by x³?
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Using the FOIL method, what is (3x + 5)(2x - 3) equal to?
Using the FOIL method, what is (3x + 5)(2x - 3) equal to?
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When multiplying a trinomial by a binomial, what is essential to do?
When multiplying a trinomial by a binomial, what is essential to do?
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What is the result of (2x² - 7x + 4)(3x² + 5x + 7) when simplified?
What is the result of (2x² - 7x + 4)(3x² + 5x + 7) when simplified?
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Study Notes
Simplifying Algebraic Expressions
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Combining Like Terms: Combine terms with the same variable and exponent.
- Example: 5x + 8 - 2x + 5 simplifies to 3x + 13.
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Distributive Property: Multiply a term outside parentheses by each term inside the parentheses.
- Example: 9(5x + 4) simplifies to 45x + 36.
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Simplifying Expressions with Parentheses: Distribute any number or negative sign in front of parentheses, then combine like terms.
- Example: 5(3x + 4) - 7x + 8 simplifies to 8x + 28.
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Multiplying Monomials: Multiply the coefficients and add the exponents of the same variables.
- Example: 4x³ * 5x² = 20x⁵.
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Dividing Monomials: Divide the coefficients and subtract the exponents of the same variables. If an exponent is negative, move the variable with the exponent to the denominator.
- Example: x⁸ / x³ = x⁵, x² / x⁵ = 1/x³, and x⁻⁷ / x⁵ = 1/x¹².
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Multiplying Binomials (FOIL): First, Outer, Inner, Last. Multiply the first terms of each binomial, then the outer terms, the inner terms, and finally the last terms. Combine like terms.
- Example: (3x + 5)(2x - 3) = 6x² + x - 15
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Multiplying a Trinomial by a Binomial: Multiply each term in the trinomial by each term in the binomial, then combine like terms.
- Example: (3x² + 2x + 4)(3x - 7) = 9x³ - 15x² - 2x - 28
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Multiplying a Trinomial by a Trinomial: Multiply each term in the first trinomial by each term in the second trinomial, then combine like terms.
- Example: (2x² - 7x + 4)(3x² + 5x + 7) = 6x⁴ - 11x³ + 9x² - 29x + 28.
Key Concepts
- Like Terms: Terms with the same variable and exponent.
- Coefficient: The number in front of a variable.
- Exponent: The number that indicates how many times a base is multiplied by itself.
- Polynomials: Expressions with one or more terms.
- Binomial: A polynomial with two terms.
- Trinomial: A polynomial with three terms.
- Monomial: A polynomial with one term.
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Description
This quiz focuses on the essential techniques for simplifying algebraic expressions. You will practice combining like terms, applying the distributive property, and manipulating monomials and binomials. Test your understanding and enhance your algebra skills!
