Algebra 1 - Simplifying Expressions Flashcards

Questions and Answers

What is a trinomial?

A polynomial with one term

A polynomial with four terms

A polynomial with three terms (correct)

A polynomial with two terms

What is a binomial?

A polynomial with four terms

A polynomial with two terms (correct)

A polynomial with three terms

A polynomial with one term

What does it mean to factor in algebra?

Using the X to simplify the polynomial

What are factors in the context of polynomials?

The result when using the X-Factor Signup and view all the answers

Match the perfect square trinomial forms:

a² + 2ab + b² = Perfect square trinomial a² - 2ab + b² = Perfect square trinomial Signup and view all the answers

What is the difference of two squares?

a² - b² = (a + b)(a - b) Signup and view all the answers

What is an algebraic expression?

A mathematical phrase involving at least one variable and sometimes numbers and operation symbols Signup and view all the answers

What is a rational exponent?

Fraction exponent Signup and view all the answers

What is an integral exponent?

Exponents that include integers (-5, -2, 3, 6, etc) Signup and view all the answers

What happens when you have a power to a power?

Multiply the exponents, base stays the same Signup and view all the answers

What is the product of powers property?

Multiply coefficients, add exponents with the same base Signup and view all the answers

What is the power of zero property?

Any non-zero power raised to the power of '0' is equal to 1 Signup and view all the answers

What is the power of one property?

Anything to the first power is itself Signup and view all the answers

What does dividing with exponents involve?

Keep the base and subtract the exponents Signup and view all the answers

Study Notes

Key Terms in Algebraic Expressions

Trinomial: A polynomial composed of three distinct terms.
Binomial: A polynomial made up of two terms.
Factor: The method of simplifying a polynomial using the X-Factor approach.
Factors: Outcomes obtained through the application of the X-Factor method.

Special Types of Polynomials

Perfect Square Trinomial: A trinomial that adheres to the format a² + 2ab + b² or a² - 2ab + b², representing a squared binomial.
Difference of Two Squares: A formula expressed as a² - b² = (a + b)(a - b), showcasing the relationship between the difference and the product of two squared terms.

Expression Characteristics

Algebraic Expression: A combination of numbers, variables, and operation symbols, including at least one variable, forming a mathematical phrase.
Rational Exponent: Refers to exponents that are expressed as fractions.
Integral Exponent: Encompasses whole numbers as exponents, including negative and positive integers such as -5, -2, 3, and 6.

Exponential Rules

Power to a Power: Involves multiplying the exponents while keeping the base unchanged.
Product of Powers: When multiplying terms with the same base, multiply their coefficients and add the exponents.
Power of Zero: Establishes that any non-zero base raised to the exponent of 0 equals 1.
Power of One: States that any base raised to the first power remains unchanged.

Division of Exponents

Dividing with Exponents: Involves retaining the base and deducting the exponents in the process of division.

Description

Test your knowledge of algebraic expressions with these flashcards focusing on key terms such as trinomials and binomials. Each card provides a definition to enhance your understanding of polynomial simplification techniques. Perfect for students looking to reinforce their algebra skills.