Lesson - Manipulating Expressions

Learning Intention: manipulate algebraic expressions by a range of techniques

Explanation:

An algebraic expression is made up of terms and operators such as +, -, x, ÷ and ().

A term is made up of numbers and letter symbols (variables) but not operators.

For example,

3a + 4b - a + 5 is an expression.

3a, 4b, a and 5 are terms in the expression

3a and a are called like terms because they both contain a number and a variable.

Example and Tasks:

1. Simplify by gathering Like terms (addition and subtraction):

4a + 5 + 2 - 3 = 6a + 2

- Explanation on Maths is Fun,
- Education Perfect: Simplifying Addition in Algebra; Adding and Subtracting Like Terms

2. Simplify by multiplication

2b x 5 = 10b; 3b x 4b = 12b²

- Education Perfect: Simplifying Multiplication using Indices;

3. Simplify by division

15c² ÷ 3c = 5c

- Education Perfect: Simplifying Division; Multiplying Algebraic Fractions

4. Expanding (CL5)

Expanding:

4(a + b) means 4 x (a + b) or:

= (a + b) + (a + b) + (a + b) + (a + b)

= a + b + a + b + a + b + a + b

= 4a + 4b

4(d - 3) = 4d -12

- Education Perfect: Expanding I; Expanding II

5. Factorising

3e + 6 = 3(e + 2); 12f² - 4f = 4f(3f - 1)

- Education Perfect: Highest Common Factor; Introduction to Factorising; Factorising Algebraic Expressions.

Grab a worksheet on the appropriate skill

Find a suitable task in your Workbook or on Education perfect.

Use the Nayland College Algebra site to access resources to practice these skills.

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