Expanding and Simplifying Expressions

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📚 Part 1: Expanding Expressions

WALT: Expand algebraic expressions using the distributive law

1. Expand the following expressions:

a) 3(2x + 4) = _______________ Answer: 6x + 12

b) 4(3a + 2) = _______________ Answer: 12a + 8

c) 5(2y - 3) = _______________ Answer: 10y - 15

d) 2(4m + 7) = _______________ Answer: 8m + 14

2. Which expression is equivalent to 6(x + 3)?

6x + 3

6x + 18 Answer: Correct

x + 18

6x + 9

3. A food stall charges $3 for each pie and $2 for each drink. Write an expression for the total cost of p pies and d drinks, then expand if there's a $5 discount on orders over $20:

Answer: Total cost = 3p + 2d; if 3p + 2d > 20, then total cost = 3p + 2d - 5.

✏️ Part 2: Simplifying Expressions

Success Criteria: I can combine like terms to simplify expressions accurately

4. Simplify by combining like terms:

a) 2x + 3y - x + 4y = _______________ Answer: x + 7y

b) 5b - 2b + 3b - b = _______________ Answer: 5b

c) 7a + 2 - 3a + 5 = _______________ Answer: 4a + 7

d) 4m + 3n - 2m + n = _______________ Answer: 2m + 4n

5. A rectangular paddock has width w metres and length (w + 5) metres. The perimeter expression is P = 2w + 2(w + 5). Expand and simplify this expression:

Answer: P = 2w + 2w + 10 = 4w + 10.

6. Expand and simplify: 2(2p + 3) + p

Answer: 4p + 6 + p = 5p + 6.