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Questions and Answers
What is the result of expanding $2(3+n)$?
What is the result of expanding $2(3+n)$?
6+3n
What do you get when you expand $-3(3-r)$?
What do you get when you expand $-3(3-r)$?
-9+r
What is the expansion of $3y(9+y)$?
What is the expansion of $3y(9+y)$?
27y + 3y^2
Expand $2(-4g-3)$?
Expand $2(-4g-3)$?
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What is the result of expanding $6k(1-2h)$?
What is the result of expanding $6k(1-2h)$?
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Study Notes
Expanding Algebraic Expressions
- Expanding involves multiplying a term outside the parentheses with each term inside.
- A common form seen in expansions is multiplying a constant by a binomial or a polynomial.
Example Expansions
- Expand 2(3+n):
- Multiply 2 by 3 and by n, resulting in 6 + 2n.
- Expand -3(3-r):
- Multiply -3 by 3 and by -r, leading to -9 + 3r (or rewritten as -9 + r in simpler terms).
- Expand 3y(9+y):
- Multiply 3y by 9 and by y, yielding 27y + 3y².
Negative and Multiple Terms
- Expand 2(-4g-3):
- Distribute 2 to each term, resulting in -8g - 6.
- Expand 6k(1-2h):
- Distributing gives 6k - 12kh.
Importance of Parentheses
- Parentheses dictate the order of operations during expansion, ensuring correct distribution of coefficients across all terms.
- Each expansion is vital for simplifying and solving algebraic equations effectively.
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