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Questions and Answers
What is the result of expanding 5(x + 4)?
What is the result of expanding 5(x + 4)?
- 5x + 20 (correct)
- 5 + 4x
- 5x + 4
- 5 + 20
Which expression represents the area of a rectangle with sides 3 and (y + 6)?
Which expression represents the area of a rectangle with sides 3 and (y + 6)?
- 3y + 6y
- 3y + 18 (correct)
- y + 18
- 3y + 6
How would you expand and simplify -2(a + 4)?
How would you expand and simplify -2(a + 4)?
- 2a - 8
- -2a - 8 (correct)
- 2a + 8
- -2a + 8
What is the expanded form of 4(z - 5)?
What is the expanded form of 4(z - 5)?
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What results from expanding y(y + 6)?
What results from expanding y(y + 6)?
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When expanding -3p(p - 4), what is the simplified result?
When expanding -3p(p - 4), what is the simplified result?
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Which of the following is NOT the correct expansion of a given expression?
Which of the following is NOT the correct expansion of a given expression?
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Which of the following expressions is expanded to y² + 36xy?
Which of the following expressions is expanded to y² + 36xy?
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Study Notes
Expanding Brackets
- The distributive rule can be used to simplify calculations involving whole numbers and algebraic expressions with brackets.
- The rule can be applied to find the area of a rectangle by breaking it down into smaller rectangles.
Example Expansions
- 15(x + 3) expands to 15x + 45
- 5(x + 4) expands to 5x + 20
- 5(y + 2) expands to 5y + 10
- 4(z - 5) expands to 4z - 20
- y(y + 6) expands to y² + 6y
- -2(a + 4) expands to -2a - 8
- -3p(p - 4) expands to -3p² + 12p
Important Notes
- When multiplying by negatives, remember that neg x pos = neg and neg x neg = pos
Exercise 1: Expanding Brackets
- The distributive rule can be applied to find the area of a rectangle by breaking it down into smaller rectangles.
- For example, 7(x + 3) expands to 7x + 21
Matching Brackets with Expanded Answers
- 2(x + 8) expands to 8x + 16
- x(x + 16) expands to x² + 16x
- 4x(x + 4) expands to 8x + 8x²
- 8(x + 2) expands to 8x + 16
- 8x(1 + x) expands to 8x + 8x²
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