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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?
- 8x + 13
- 5x + 5
- 3x + 3
- 3x + 13 (correct)
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)?
- Distribute negative signs throughout the expression.
- Add both terms together only.
- Multiply the outer terms by 9.
- Multiply each term inside the parentheses by 9. (correct)
How do you simplify the expression 5(3x + 4) - 7x + 8?
How do you simplify the expression 5(3x + 4) - 7x + 8?
- 15x + 20
- 5x + 28
- 8x + 28 (correct)
- 8x + 4
What is the product of the monomials 4x³ and 5x²?
What is the product of the monomials 4x³ and 5x²?
What is the result of dividing x⁸ by x³?
What is the result of dividing x⁸ by x³?
Using the FOIL method, what is (3x + 5)(2x - 3) equal to?
Using the FOIL method, what is (3x + 5)(2x - 3) equal to?
When multiplying a trinomial by a binomial, what is essential to do?
When multiplying a trinomial by a binomial, what is essential to do?
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?
Flashcards
Like Terms
Like Terms
Terms that have the same variable and exponent. Example: 5x and 2x are like terms, but 5x and 5x² are not.
Coefficient
Coefficient
The number in front of a variable. Example: In the term 7x, 7 is the coefficient.
Exponent
Exponent
A small number written above and to the right of a base. It indicates how many times the base is multiplied by itself. Example: In 5², the exponent is 2.
Polynomial
Polynomial
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Binomial
Binomial
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Trinomial
Trinomial
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Monomial
Monomial
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Simplifying Algebraic Expressions
Simplifying Algebraic Expressions
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Study Notes
Simplifying Algebraic Expressions
- Combining Like Terms: Combine terms with the same variable and exponent.
- Example: 5x + 8 - 2x + 5 simplifies to 3x + 13.
- Distributive Property: Multiply a term outside parentheses by each term inside the parentheses.
- Example: 9(5x + 4) simplifies to 45x + 36.
- 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.
- Multiplying Monomials: Multiply the coefficients and add the exponents of the same variables.
- Example: 4x³ * 5x² = 20x⁵.
- 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.
- 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
- 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
- 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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