☰ Year plan · Mathematics

Algebraic expressions and formulas

Week 6 Β· Algebraic expressions and formulas: terms, like terms, simplifying and evaluating Β· 3 lessons
3

Brackets and the distributive property: adding expressions and evaluating

Mathematics Prep 1 Term 1, Unit 2, Lesson 1
GoalRemove brackets with the distributive property, add expressions and find the value for a given number.
New words
distributive property Β· a(b + c) = ab + acexpand Β· remove brackets by multiplying every term insidesubstitute Β· replace a letter by a numbervalue Β· the number an expression gives after substituting
Explanation

The distributive property says a(b + c) = ab + ac and a(b βˆ’ c) = ab βˆ’ ac. Multiply the number outside by every term inside: 3(x βˆ’ 4) = 3x βˆ’ 12. A minus sign before a bracket changes every sign inside: βˆ’(x βˆ’ y) = βˆ’x + y, and βˆ’(βˆ’x) = x. To add or subtract expressions, remove the brackets and collect like terms: (3x + 5) + (2x βˆ’ 7) = 5x βˆ’ 2. To find a value, substitute the number for the letter: for 3x βˆ’ 5 with x = 4, we get 3 Γ— 4 βˆ’ 5 = 7.

Ζ’Formula
a(b + c) = ab + ac
Also a(b βˆ’ c) = ab βˆ’ ac and βˆ’(x βˆ’ y) = βˆ’x + y.
Worked examples
Expand 3(x βˆ’ 4): multiply 3 Γ— x = 3x and 3 Γ— 4 = 12, so 3x βˆ’ 12. Expand 2(3a + 5) = 6a + 10. Check with a = 1: 2(3 + 5) = 16 and 6 + 10 = 16.
A minus before a bracket. βˆ’(x βˆ’ y) = βˆ’x + y. And 5 βˆ’ (2x βˆ’ 3) = 5 βˆ’ 2x + 3 = 8 βˆ’ 2x. Subtract expressions: (4x + 1) βˆ’ (x βˆ’ 3) = 4x + 1 βˆ’ x + 3 = 3x + 4.
x4x + 4
524
1044
1564
Three children get x LE, x + 4 LE and 2x LE. The total is x + (x + 4) + 2x = 4x + 4. If x = 10, the total is 4 Γ— 10 + 4 = 44 LE. The table shows more values.
Class activity

Check by numbers. With a grown-up, pick x = 2. Work out 3(x + 4) and also 3x + 12. Do they agree? Try x = 5. Then try a wrong expansion, 3x + 4, and see that it disagrees.

Practice
1
Expand 5(2x βˆ’ 3).
2
Expand βˆ’(3x βˆ’ 2).
3
Add (4x + 3) and (x βˆ’ 8).
4
Find the value of 3x βˆ’ 5 when x = 6.
5
Seif writes 3(x βˆ’ 4) = 3x βˆ’ 4. What is wrong? Check with x = 5.