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Questions and Answers
Which expression is equivalent to $4(3n - 4) + 2$?
Which expression is equivalent to $4(3n - 4) + 2$?
- $7n - 18$
- $12n - 18$
- $12n - 14$ (correct)
- $7n - 14$
What is the expanded form of the expression $5(4a + 1)$?
What is the expanded form of the expression $5(4a + 1)$?
- $9a+6$
- $9a + 1$
- $20a + 5$ (correct)
- $20a + 1$
Which expression is equivalent to $4x + 8y$?
Which expression is equivalent to $4x + 8y$?
- $5y + 2(2x + 3y)$
- $2(2y) + 2(2y) + 2(2x)$ (correct)
- $4(x + 3y) - 4y$
- All of the above
If $x = 4$ and $y = 5$, does $3(x + y) = 3x + 3y$?
If $x = 4$ and $y = 5$, does $3(x + y) = 3x + 3y$?
If $x = 4$ and $y = 5$, does $5(-2x + 4) + 2(x + 3) = 10x + 20 + 2x + 5$?
If $x = 4$ and $y = 5$, does $5(-2x + 4) + 2(x + 3) = 10x + 20 + 2x + 5$?
If $y = 5$, does $9y + 5(2y - 1) = 19y - 5$?
If $y = 5$, does $9y + 5(2y - 1) = 19y - 5$?
Which expression will represent the area of MPR, assuming it is a rectangle with sides of length $a$ and $b$?
Which expression will represent the area of MPR, assuming it is a rectangle with sides of length $a$ and $b$?
Which expression will represent the area of the lunch room, assuming it is a square with sides of length $s$?
Which expression will represent the area of the lunch room, assuming it is a square with sides of length $s$?
What expression represents the perimeter of a rectangle with length $l$ and width $w$?
What expression represents the perimeter of a rectangle with length $l$ and width $w$?
If the MPR has sides of length $a$ and $b$, and the Lunch Room is a square with sides of length $s$, what is the expression for the combined area?
If the MPR has sides of length $a$ and $b$, and the Lunch Room is a square with sides of length $s$, what is the expression for the combined area?
Flashcards
Expanded Form
Expanded Form
To expand an expression, multiply each term inside the parentheses by the term outside.
Combining Like Terms
Combining Like Terms
The process of simplifying an expression by combining terms with the same variable and exponent.
Distributive Property
Distributive Property
A property indicating how multiplication affects addition or subtraction
Substitution
Substitution
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Factoring
Factoring
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Equivalent Expressions
Equivalent Expressions
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Study Notes
- The distributive property, factoring, and combining like terms can be used to find equivalent expressions.
Equivalent Expressions
- To find equivalent expressions, use the distributive property, factoring, and combining like terms.
- Expressions can be rewritten into expanded from by using the distributive property.
- Expressions of the form a(b+c) can be expanded to ab+ac
- To determine if expressions are equivalent, substitute given values for the variables and evaluate.
Problems
- x² + 6x is an expression for which an equivalent expression needs to be found.
- 4(3n -4) +2 is an expression for which an equivalent expression needs to be found.
- 4(2x-4) - 2(5x-4) is an expression for which an equivalent expression needs to be found.
- 5(4a +1) is an expression that should be re-written into expanded form.
- 4(7x - 4) is an expression that should be re-written into expanded form.
- -2(3b + 3) is an expression that should be re-written into expanded form.
- Jimmy wrote the expression 4x+8y and his classmates wrote expressions that they felt were equivalent.
- Henry: 5y + 2(2x + 3y)
- Foster: 2(2y) + 2(2y) + 2(2x)
- Alex: 4(x + 3y) - 4y
Checking for equivalence
- Check if 3(x + y) = 3x + 3y when x=4, y= 5.
- Check if 5(-2x + 4) + 2(x + 3) = 10x +20 + 2x +5 when x=4, y= 5.
- Check if 9y + 5(2y - 1) = 19y -5 when x=4, y= 5.
- Image provided to answer questions about expressions for area and perimeter of MPR and lunch room.
- Write an expression that represents the area of the MPR.
- Write an expression to represent the area of the Lunch Room
- Write an expression for the total area of the MPR and the Lunch Room
- Write an expression to represent the perimeter of the MPR and the Lunch Room combined.
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