Algebraic Operations Flashcards

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Questions and Answers

What is combining like terms?

The process of simplifying an expression by adding together or subtracting terms that have the same variable factors.

What does factoring algebraic expressions involve?

Reformatting an expression as a product of two or more simpler expressions.

What is substitution in algebra?

The process of replacing a variable in an expression with another value.

What is the key principle in solving equations?

Always perform the same operation on both sides of the equal sign. Signup and view all the answers

What happens when you multiply or divide an inequality by a negative number?

The direction of the inequality sign is reversed Signup and view all the answers

How do you solve for one unknown in terms of another?

Isolate the desired variable on one side of the equation and move all the constants and other variables to the other side. Signup and view all the answers

What are sequences in mathematics?

Lists of numbers or formulas that define each element. Signup and view all the answers

What does the FOIL method stand for?

First, Outer, Inner, Last. Signup and view all the answers

The product of two missing terms in factoring the product of binomials will be the last term in the polynomial.

True Signup and view all the answers

How can the difference of squares be factored?

Any polynomial of the form $a^2 - b^2$ can be factored into the form $(a - b)(a + b)$. Signup and view all the answers

Which polynomial is equal to $(a + b)^2$?

$a^2 + 2ab + b^2$ Signup and view all the answers

What is the general form of quadratic equations?

An equation of the form: $f(x) = ax² + bx + c = 0$, where $a eq 0$. Signup and view all the answers

What is the backsolving strategy?

Substituting each answer choice from a multiple choice question into the equation until one satisfies the equation. Signup and view all the answers

What does picking numbers strategy involve?

Choosing a number for a variable in an algebraic expression problem to simplify the problem. Signup and view all the answers

What should you do if the first number picked does not lead to a single correct answer?

Either pick a new number or guess strategically among the answers that haven't been eliminated. Signup and view all the answers

Study Notes

Combining Like Terms

Simplifies expressions by adding or subtracting terms with the same variables.

Factoring Algebraic Expressions

Involves rewriting expressions as a product of simpler expressions.
Uses the distributive law to extract common factors.

Substitution

Replaces a variable in an expression with another value.
Useful for evaluating expressions or expressing them in terms of other variables.

Solving Equations

Requires performing the same operation on both sides of the equal sign to maintain equality.

Inequalities

Solutions typically represent a range of values instead of a single value.
Be cautious when multiplying or dividing by a negative number, as it reverses the inequality sign.

Solving for One Unknown

Involves isolating a desired variable on one side of the equation.
All constants and other variables are moved to the opposite side.

Sequence

A sequence is a list of numbers or formulas that defines each element in a structured way.

FOIL Method

A technique to multiply two binomials by summing the products of the First, Outer, Inner, and Last terms.

Factoring the Product of Binomials

Polynomials can often be broken down into two binomials, each with an x term.
The last term of the polynomial corresponds to the product of the two missing terms.
The sum of these missing terms equates to the coefficient of the second term.

Factoring the Difference of Squares

Any polynomial in the form a² - b² can be factored into (a - b)(a + b).

Factoring Specific Polynomial Forms

For a² + 2ab + b², the factorization is (a + b)² when the sign before 2ab is positive.
For a² - 2ab + b², it factors as (a - b)² when the sign is negative.

Quadratic Equations

Represented by the equation f(x) = ax² + bx + c = 0, where a is not equal to zero.
Can be solved by factoring the expression and setting factors equal to zero.

Backsolving Strategy

Involves substituting each answer choice into the equation to determine which satisfies it.

Picking Numbers Strategy

Involves selecting a number for a variable in algebraic problems to reduce abstraction.
Helps evaluate answer choices by using the selected number in place of the variable.

Using Picking Numbers for Solving

If the initial number does not lead to a unique solution, either select a new number or strategically guess among remaining answer choices.

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Description

Test your understanding of key algebraic operations with these flashcards. You'll learn about combining like terms, factoring algebraic expressions, and substitution, helping you grasp essential concepts in algebra.