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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?
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 $a + (c + x)$?
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 $-3(4x - 5)$?
Which of the following correctly expands $(w + y)^3$?
Which of the following correctly expands $(w + y)^3$?
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Which of the following is a prime expression?
Which of the following is a prime expression?
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Which of the following is the correct sum for $3
adical{2} +
adical{8}$?
Which of the following is the correct sum for $3 adical{2} + adical{8}$?
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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?
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Which of the following is a like radical with $-2
adical{3}5$?
Which of the following is a like radical with $-2 adical{3}5$?
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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?
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Which of the following is the conjugate of $
adical{2} - 7$?
Which of the following is the conjugate of $ adical{2} - 7$?
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What is twice w decreased by four?
What is twice w decreased by four?
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What is the product of x and y if it is twenty?
What is the product of x and y if it is twenty?
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Evaluate $3xy + z^3$ when it is equal to -25.
Evaluate $3xy + z^3$ when it is equal to -25.
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What does the expression $12z^2 / 2y^2$ simplify to?
What does the expression $12z^2 / 2y^2$ simplify to?
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What is $(-2x^2)^2 · x^4y$ equal to?
What is $(-2x^2)^2 · x^4y$ equal to?
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Simplify $6w^2z^{-1} / 3wz^4$.
Simplify $6w^2z^{-1} / 3wz^4$.
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What does $(w + 4) - (w^2 + 5w + 2)$ simplify to?
What does $(w + 4) - (w^2 + 5w + 2)$ simplify to?
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What does $(4a + b)(a - 5b)$ expand to?
What does $(4a + b)(a - 5b)$ expand to?
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Expand $(2x - y)(2x + y)$.
Expand $(2x - y)(2x + y)$.
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What does $(2q + 3)^2$ expand to?
What does $(2q + 3)^2$ expand to?
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Simplify $8x^3 + 3x^2 / 2x$.
Simplify $8x^3 + 3x^2 / 2x$.
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What does $x^3 - 6x^2 + 9x$ factor to?
What does $x^3 - 6x^2 + 9x$ factor to?
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What does $9y^2 - 121$ factor to?
What does $9y^2 - 121$ factor to?
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Factor $a^5 - b^5$.
Factor $a^5 - b^5$.
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What does $x^4 - 81$ factor to?
What does $x^4 - 81$ factor to?
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What does $x^2 - 4x - 21$ factor to?
What does $x^2 - 4x - 21$ factor to?
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What does $3x^2 + 19x + 20$ factor to?
What does $3x^2 + 19x + 20$ factor to?
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What does $w^2 - 12w + 36$ factor to?
What does $w^2 - 12w + 36$ factor to?
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What does $x/x^2 - 6x$ simplify to?
What does $x/x^2 - 6x$ simplify to?
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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?
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Simplify $3/x + 4 + 4/x - 3$.
Simplify $3/x + 4 + 4/x - 3$.
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What is $
adical{12} + 2
adical{27}$ equal to?
What is $ adical{12} + 2 adical{27}$ equal to?
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What is $^3
adical{3x} imes ^3
adical{9x^4}$?
What is $^3 adical{3x} imes ^3 adical{9x^4}$?
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What is $^4
adical{12x^3} / ^4
adical{6x^7}$?
What is $^4 adical{12x^3} / ^4 adical{6x^7}$?
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What is $9/x -
adical{7}$?
What is $9/x - adical{7}$?
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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
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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!
