Podcast
Questions and Answers
In the expression $2(3 + 5) - 4^2$, which operation should be done first?
In the expression $2(3 + 5) - 4^2$, which operation should be done first?
- Parentheses (correct)
- Addition
- Subtraction
- Exponentiation
Which of the following algebraic properties was applied to the expression $(a + c) + x$ to get the expression $a + (c + x)$?
Which of the following algebraic properties was applied to the expression $(a + c) + x$ to get the expression $a + (c + x)$?
- Associative (correct)
- Identity
- Distributive
- Commutative
Which of the following shows the distributive property done correctly on the expression $-3(4x - 5)$?
Which of the following shows the distributive property done correctly on the expression $-3(4x - 5)$?
- -3(4x + 5)
- -12x + 15 (correct)
- -3(4x) - 3(-5)
- -12x - 15
Which of the following correctly expands $(w + y)^3$?
Which of the following correctly expands $(w + y)^3$?
Which of the following is a prime expression?
Which of the following is a prime expression?
Which of the following is the correct sum for $3
adical{2} +
adical{8}$?
Which of the following is the correct sum for $3 adical{2} + adical{8}$?
What is the term for the root that matches the radicand in sign?
What is the term for the root that matches the radicand in sign?
Which of the following is a like radical with $-2
adical{3}5$?
Which of the following is a like radical with $-2 adical{3}5$?
In order to multiply radicals, which of the following needs to be true?
In order to multiply radicals, which of the following needs to be true?
Which of the following is the conjugate of $
adical{2} - 7$?
Which of the following is the conjugate of $ adical{2} - 7$?
What is twice w decreased by four?
What is twice w decreased by four?
What is the product of x and y if it is twenty?
What is the product of x and y if it is twenty?
Evaluate $3xy + z^3$ when it is equal to -25.
Evaluate $3xy + z^3$ when it is equal to -25.
What does the expression $12z^2 / 2y^2$ simplify to?
What does the expression $12z^2 / 2y^2$ simplify to?
What is $(-2x^2)^2 · x^4y$ equal to?
What is $(-2x^2)^2 · x^4y$ equal to?
Simplify $6w^2z^{-1} / 3wz^4$.
Simplify $6w^2z^{-1} / 3wz^4$.
What does $(w + 4) - (w^2 + 5w + 2)$ simplify to?
What does $(w + 4) - (w^2 + 5w + 2)$ simplify to?
What does $(4a + b)(a - 5b)$ expand to?
What does $(4a + b)(a - 5b)$ expand to?
Expand $(2x - y)(2x + y)$.
Expand $(2x - y)(2x + y)$.
What does $(2q + 3)^2$ expand to?
What does $(2q + 3)^2$ expand to?
Simplify $8x^3 + 3x^2 / 2x$.
Simplify $8x^3 + 3x^2 / 2x$.
What does $x^3 - 6x^2 + 9x$ factor to?
What does $x^3 - 6x^2 + 9x$ factor to?
What does $9y^2 - 121$ factor to?
What does $9y^2 - 121$ factor to?
Factor $a^5 - b^5$.
Factor $a^5 - b^5$.
What does $x^4 - 81$ factor to?
What does $x^4 - 81$ factor to?
What does $x^2 - 4x - 21$ factor to?
What does $x^2 - 4x - 21$ factor to?
What does $3x^2 + 19x + 20$ factor to?
What does $3x^2 + 19x + 20$ factor to?
What does $w^2 - 12w + 36$ factor to?
What does $w^2 - 12w + 36$ factor to?
What does $x/x^2 - 6x$ simplify to?
What does $x/x^2 - 6x$ simplify to?
What does $5/x + 2$ divided by $6/x^2 - x - 6$ equal?
What does $5/x + 2$ divided by $6/x^2 - x - 6$ equal?
Simplify $3/x + 4 + 4/x - 3$.
Simplify $3/x + 4 + 4/x - 3$.
What is $
adical{12} + 2
adical{27}$ equal to?
What is $ adical{12} + 2 adical{27}$ equal to?
What is $^3
adical{3x} imes ^3
adical{9x^4}$?
What is $^3 adical{3x} imes ^3 adical{9x^4}$?
What is $^4
adical{12x^3} / ^4
adical{6x^7}$?
What is $^4 adical{12x^3} / ^4 adical{6x^7}$?
What is $9/x -
adical{7}$?
What is $9/x - adical{7}$?
Flashcards
Associative Property
Associative Property
Changing the grouping of numbers in an addition problem doesn't change the result.
Distributive Property
Distributive Property
Multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the products.
Prime Expression
Prime Expression
An expression that can't be factored further.
Simplifying Radicals
Simplifying Radicals
Signup and view all the flashcards
Like terms
Like terms
Signup and view all the flashcards
Conjugates
Conjugates
Signup and view all the flashcards
Multiplying Radicals
Multiplying Radicals
Signup and view all the flashcards
Order of Operations (PEMDAS)
Order of Operations (PEMDAS)
Signup and view all the flashcards
Algebraic Expressions
Algebraic Expressions
Signup and view all the flashcards
Evaluating Expressions
Evaluating Expressions
Signup and view all the flashcards
Simplifying Expressions
Simplifying Expressions
Signup and view all the flashcards
Polynomial Expressions
Polynomial Expressions
Signup and view all the flashcards
Factoring
Factoring
Signup and view all the flashcards
Rational Expressions
Rational Expressions
Signup and view all the flashcards
Simplifying Rational Expressions
Simplifying Rational Expressions
Signup and view all the flashcards
Principal Root
Principal Root
Signup and view all the flashcards
Quadratic Equation
Quadratic Equation
Signup and view all the flashcards
Study Notes
Operations and Properties
- Prioritize operations in expressions: Parentheses first as seen in 2(3 + 5) − 4^2.
- The associative property allows rearranging grouping in addition, exemplified by (a + c) + x becoming a + (c + x).
Distributive Property
- Distributing -3 across (4x − 5) results in -12x + 15.
- Correctly expanding (w + y)^3 gives w^3 + 3w^2y + 3wy^2 + y^3.
Radicals and Like Terms
- Identify primes: x^2 + 16 is a prime expression.
- Simplifying radicals: The sum of 3√2 + √8 equals 5√2.
- Principal root refers to the root matching the radicand's sign.
Conjugates and Like Radicals
- Conjugate of √2 - 7 is √2 + 7.
- A like radical for -2^3√5 is 12^3√5.
Multiplying Radicals
- Multiplication of radicals requires the same indices.
Algebraic Expressions and Operations
- "Twice w decreased by four" translates to 2w - 4.
- The product of x and y expressed as xy = 20.
- Evaluating expressions: 3xy + z^3 equals -25.
Simplifying Expressions
- 12z^2/2y^2 simplifies to 3/2.
- (-2x^2)^2 · x^4y results in 4x⁸y.
- Simplifying 6w^2z^-1/3wz^4 yields 2w/z⁵.
Polynomial Expressions
- (w + 4) − (w^2 + 5w + 2) simplifies to -w² - 4w + 2.
- The expansion of (4a+b)(a−5b) gives 4a² - 19ab - 5b².
- Expanding (2x − y)(2x + y) results in 4x² - y².
- Squaring (2q + 3) results in 4q² + 12q + 9.
Factoring and Roots
- 8x^3 + 3x^2/2x simplifies to 4x² + 3x.
- The expression x^3 − 6x^2 + 9x factors as x(x - 3)².
- 9y² - 121 factors to (3y + 11)(3y - 11).
- a^5 - b^5 is factored as (a - b)(a⁴ + a³b + a²b² + ab³ + b⁴).
- x^4 - 81 factors to (x² + 9)(x + 3)(x - 3).
- The quadratic x² - 4x - 21 factors as (x + 3)(x - 7).
- 3x² + 19x + 20 factors to (3x + 4)(x + 5).
- w² - 12w + 36 factors to (w - 6)².
Rational Expressions and Equations
- The expression x/x² - 6x simplifies to 1/x - 6 (note x ≠ 0).
- 5/x + 2 divided by 6/x² - x - 6 results in 5(x - 3)/6 (note x ≠ -2, 3).
- The combined fractions 3/x + 4 + 4/x - 3 simplify to (7x + 7)/((x + 4)(x - 3)).
Simplifying Radicals
- The expression √12 + 2√27 simplifies to 8√3.
- Combined cube roots ^3√3x * ^3√9x^4 simplifies to 3x^3√x².
- Dividing fourth roots ^4√12x³/^4√6x⁷ simplifies to 1/x ^4√2.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of Algebra 2 concepts with this flashcard quiz based on the Abeka curriculum. The quiz covers essential operations, properties, and expressions important for mastering Algebra 2. Perfect for students preparing for their tests!
