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Questions and Answers
Which expression represents the expansion of $-3(x + 5)$?
Which expression represents the expansion of $-3(x + 5)$?
- $-3x - 8$
- $-3x + 5$
- $-3x + 15$
- $-3x - 15$ (correct)
What is the result of expanding $4(x + 2)$ using the distributive property?
What is the result of expanding $4(x + 2)$ using the distributive property?
- $x + 8$
- $4x - 8$
- $4x + 8$ (correct)
- $x - 8$
Expand $-2(y + 1)$ and simplify the expression.
Expand $-2(y + 1)$ and simplify the expression.
- $-2y - 1$
- $-2y + 2$
- $-2y + 1$
- $-2y - 2$ (correct)
What is the expanded form of $5(k - 3)$ using the distributive property?
What is the expanded form of $5(k - 3)$ using the distributive property?
When expanding $-4w(3w - 1)$, what is the resulting expression?
When expanding $-4w(3w - 1)$, what is the resulting expression?
Expand and simplify the expression $4w - 2 - 2(2w + 7)$.
Expand and simplify the expression $4w - 2 - 2(2w + 7)$.
What is the result of expanding $3[2k - 2 + k]$?
What is the result of expanding $3[2k - 2 + k]$?
What is the correct expansion of $2b(3b - 5)$?
What is the correct expansion of $2b(3b - 5)$?
When simplifying the expression $-5y(3y - 7y - 2)$, what is the final result?
When simplifying the expression $-5y(3y - 7y - 2)$, what is the final result?
What is the result of expanding $-8(2 - d)$?
What is the result of expanding $-8(2 - d)$?
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Study Notes
Distributive Property
- The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
- For example, 4(x + 2) = 4x + 8.
- This property can be used to expand and simplify algebraic expressions.
Expanding Expressions
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Examples of expanding expressions using the distributive property:
- 4(x + 2) = 4x + 8
- 5(k - 3) = 5k - 15
- -2(y + 1) = -2y - 2
- -8(2 - d) = -16 + 8d
- 5(2t – 3) = 10t - 15
- – (4y – 5) = -4y + 5
- y(y – 4) = y² - 4y
- r(r + 5) = r² + 5r
- x (2x – 5) = 2x² - 5x
- q(-4q + 8) = -4q² + 8q
- z(-3z + 2) = -3z² + 2z
- m(-m - 5) = -m² - 5m
- 2b(3b – 5) = 6b² - 10b
- -4w(3w - 1) = -12w² + 4w
- 2x(-4x + 3) = -8x² + 6x
- (4k + 7)(-3k) = -12k² - 21k
- n - 5 × 4 = 4n - 20
- (7m + 6)(-4) = -28m - 24
- (7 + c)(3c) = 21c + 3c²
- (4k + 7)(-3k) = -12k² - 21k
- 2(a + 5a + 3) = 2a + 10a + 6
- 4x(x + x - 3) = 4 x² + 4x² - 12x
- -5y(3y - 7y - 2) = -15y² + 35y² + 10y
- (2y + 3y - 1)(4y) = 8y² + 12y² - 4y
Expanding and simplifying expressions
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When expanding and simplifying expressions, combine like terms.
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Examples of expanding and simplifying expressions:
- 3x + 2 + 4(x - 5) = 3x + 2 + 4x - 20 = 7x - 18
- -4y + 1 + 2(2y - 3) = -4y + 1 +4y - 6 = -5
- 2u + v - 3(u – v) = 2u + v - 3u + 3v = -u + 4v
- 4w – 2 – 2(2w + 7) = 4w – 2 – 4w - 14 = -16
- 3[x + 2x - 4] = 3x + 6x - 12 = 9x - 12
- 3[2k - 2 + k] = 6k - 6 + 3k = 9k - 6
- 2[-h - 2h - 1] = -2h - 4h - 2 = -6h - 2
Representing Perimeter and Area
- To find the perimeter of a rectangle, add up the lengths of all sides.
- To find the area of a rectangle, multiply the length by the width.
Simplifying Expressions with Multiple Operations
- 3y - 2 - 2(4 - 2y) + (6 - 7y) = 3y - 2 - 8 +4y + 6 - 7y = y - 4
- 4k(k - 3) - 2(k² - 3k) + 4 - (k² - 3k) = 4k² - 12k - 2k² + 6k + 4 - k² + 3k = k² - 3k + 4
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