Lesson - Manipulating Expressions
Learning Intention: manipulate algebraic expressions by a range of techniques
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 ().
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.
A term is made up of numbers and letter symbols (variables) but not operators.
For example,
For example,
3a + 4b - a + 5 is an expression.
3a + 4b - a + 5 is an expression.
3a, 4b, a and 5 are terms in the 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.
3a and a are called like terms because they both contain a number and a variable.
Example and Tasks:
Example and Tasks:
1. Simplify by gathering Like terms (addition and subtraction):
1. Simplify by gathering Like terms (addition and subtraction):
4a + 5 + 2 - 3 = 6a + 2
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
2. Simplify by multiplication
2b x 5 = 10x; 3b x 4b = 12b²
2b x 5 = 10x; 3b x 4b = 12b²
Education Perfect: Simplifying Multiplication using Indices;
3. Simplify by division
3. Simplify by division
15c² ÷ 3c = 5c
15c² ÷ 3c = 5c
Education Perfect: Simplifying Division; Multiplying Algebraic Fractions
4. Expanding (CL5)
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
4(d - 3) = 4d -12
Education Perfect: Expanding I; Expanding II
5. Factorising
5. Factorising
3e + 6 = 3(e + 2); 12f² - 4f = 4f(3f - 1)
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.