Podcast
Questions and Answers
Which method is best suited for expanding the expression $3x(2x + 5y - 4)$?
Which method is best suited for expanding the expression $3x(2x + 5y - 4)$?
- Difference of squares
- Distributive property (correct)
- Perfect squares
- Factoring by grouping
What is the first step in factoring the expression $12x^3 + 18x^2 - 24x$ completely?
What is the first step in factoring the expression $12x^3 + 18x^2 - 24x$ completely?
- Factoring by grouping
- Using the difference of squares
- Factoring out the greatest common factor (correct)
- Using perfect squares
Which of the following expressions is a perfect square trinomial?
Which of the following expressions is a perfect square trinomial?
- $x^2 + 4x + 2$
- $x^2 + 8x + 16$ (correct)
- $x^2 + 10x + 20$
- $x^2 + 6x + 6$
What is the factored form of the expression $x^2 - 9$?
What is the factored form of the expression $x^2 - 9$?
Which of the following is the correct expansion of $(2x - 3)^2$?
Which of the following is the correct expansion of $(2x - 3)^2$?
Factor the following expression completely: $2x^2 + 7x + 3$.
Factor the following expression completely: $2x^2 + 7x + 3$.
Which expression is equivalent to $x^3 - x$ after factoring completely?
Which expression is equivalent to $x^3 - x$ after factoring completely?
What is the value of $k$ if $x^2 + kx + 25$ is a perfect square trinomial?
What is the value of $k$ if $x^2 + kx + 25$ is a perfect square trinomial?
Given the equation $(x + a)(x + b) = x^2 + 5x + 6$, find the values of $a$ and $b$.
Given the equation $(x + a)(x + b) = x^2 + 5x + 6$, find the values of $a$ and $b$.
After factoring out the greatest common factor, what is the remaining expression when factoring $6x^2y + 9xy^2 - 12xy$?
After factoring out the greatest common factor, what is the remaining expression when factoring $6x^2y + 9xy^2 - 12xy$?
Flashcards
Distributive Property
Distributive Property
Multiplying each term inside a bracket by the term outside the bracket.
Perfect Squares
Perfect Squares
Algebraic identities derived from squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2 and (a - b)^2 = a^2 - 2ab + b^2.
Difference of Squares
Difference of Squares
Algebraic identity where the difference of two squares factors into (a + b)(a - b).
Proving Identities
Proving Identities
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Factoring by Common Factor
Factoring by Common Factor
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Factoring by Grouping
Factoring by Grouping
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Factoring Trinomials
Factoring Trinomials
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Study Notes
- An upcoming test on special products, expanding, and factoring, covering the entire unit is scheduled for Tuesday, March 4th.
- Key topics include expanding using the distributive property.
- Expanding using special products: perfect squares and difference of squares will be tested.
- Proving identities will be assessed.
- Factoring by common factor is a key area.
- Factoring by grouping will be evaluated.
- Factoring by difference of squares is important.
- Factoring using perfect squares is a focus.
- Factoring trinomials where a = 1 or a ≠1 will be tested.
- Factoring by combining common factors with other techniques is included.
- Relevant textbook chapters for review are Chapter 3 "Expansion and Factorization of Algebraic Expressions" (pg. 69-86) and "Quadratic Factorization and Equations" (pg. 88-92) from Dimensions 8A Textbook and Workbook.
- Completed worksheets under the factoring section should be used for revision.
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