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Questions and Answers
Which of the following expressions represents the square of a binomial?
Which of the following expressions represents the square of a binomial?
- $a^3 + b^3$
- $a^2 - b^2$
- $(a + b)^2$ (correct)
- $(a + b)(a - b)$
When solving a system of equations algebraically, you arrive at the statement $5 = 9$. How would you classify this system?
When solving a system of equations algebraically, you arrive at the statement $5 = 9$. How would you classify this system?
- Mutually exclusive
- Consistent and independent
- Consistent and dependent
- Inconsistent (correct)
What is the result of the product $(x + 3)(x - 3)$?
What is the result of the product $(x + 3)(x - 3)$?
- $x^2 + 9$
- $x^2 + 6x + 9$
- $x^2 - 9$ (correct)
- $x^2 - 6x + 9$
A system of equations, when graphed, results in two lines that are the same. How is this system classified?
A system of equations, when graphed, results in two lines that are the same. How is this system classified?
Which of the following is the expanded form of $(2x - 1)^2$?
Which of the following is the expanded form of $(2x - 1)^2$?
If solving a system of equations leads to the statement $7 = 7$, how is the system best described?
If solving a system of equations leads to the statement $7 = 7$, how is the system best described?
Which expression represents the product of the sum and difference of two terms?
Which expression represents the product of the sum and difference of two terms?
A system of equations has one unique solution. When graphed, what does this indicate about the lines?
A system of equations has one unique solution. When graphed, what does this indicate about the lines?
Simplify the expression: $(3x + 2)^2$
Simplify the expression: $(3x + 2)^2$
What does it mean to 'solve' a system of equations?
What does it mean to 'solve' a system of equations?
Flashcards
Square of a Binomial
Square of a Binomial
(a + b)² = a² + 2ab + b² or (a - b)² = a² - 2ab + b²
Sum and Difference
Sum and Difference
(a + b)(a - b) = a² - b²
Solve (in equations)
Solve (in equations)
Find the solution(s), or state “no solutions" or "infinitely many solutions."
Inconsistent System
Inconsistent System
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Consistent and Dependent System
Consistent and Dependent System
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Consistent and Independent System
Consistent and Independent System
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Study Notes
- Patterns in multiplication of binomials can be recognized.
Square of a Binomial
- (a + b)² = a² + 2ab + b²
- (a - b)² = a² - 2ab + b²
Sum and Difference
- (a + b)(a - b) = a² - b²
- To solve, find the solution or state "no solutions" or "infinitely many solutions".
- Classify using the following vocabulary terms:
Inconsistent
- There is no common solution.
- Lines are parallel when graphed.
- When solved algebraically, you get a statement that is never true (ex. 3 = 7).
Consistent and Dependent
- System results in the same line when graphed.
- Same equation when equations are put in slope-intercept form.
- When solved algebraically, the statement is always true (ex. 4 = 4).
Consistent and Independent
- There is one common solution.
- When graphed, there will be one intersection.
- When solved algebraically, you get one solution, a specific point (x,y).
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Description
Explore binomial multiplication patterns including the square of a binomial and sum and difference. Learn to classify systems of equations as inconsistent, consistent and dependent, or consistent and independent based on their solutions and graphical representations. Understand how to identify these systems algebraically and graphically.
