05/04/2023
TOPIC: ALGEBRAIC EXPRESSIONS
Algebraic language
• Revise the following:
− Recognise and identify conventions for writing algebraic expressions.
− Identify and classify like and unlike terms in algebraic expressions.
− Recognise and identify coefficients and exponents in algebraic expressions.
− Recognise and differentiate between monomials, binomials and trinomials.
Expand and simplify algebraic expressions:
• Revise the following: using the commutative, associative and distributive laws for rational numbers and laws of exponents to:
− Add and subtract like terms in algebraic expressions.
− Multiply integers and monomials by: monomials, binomials, trinomials.
− Divide the following by integers or monomials: monomials, binomials, trinomials.
− Simplify algebraic expressions involving the above operations.
− Determine the squares, cubes, square roots and cube roots of single algebraic terms or like algebraic terms.
NB. ENSURE THAT COMMON FRACTIONS AND DECIMAL FRACTIONS ARE PART OF CALCULATIONS WITH EXPRESSIONS (Page 122 and 123 of CAPS)
• Extend the above algebraic manipulations to include:
− Multiply integers and monomials by polynomials.
− Divide polynomials by integers or monomials.
− The product of two binomials.
− The square of a binomial.
• Determine the numerical value of algebraic expressions by substitution
Factorise algebraic expressions:
• Factorise algebraic expressions that involve:
− Common factors
− Difference of two squares
− Trinomials of the form:
✓ 𝑥2 + 𝑏𝑥 + 𝑐
✓ 𝑎𝑥 2 + 𝑏𝑥 + 𝑐, where a is a common factor
• Simplify algebraic expressions that involve the above factorisation processes
• Simplify algebraic fractions using factorisation