Algebraic techniques - advanced

This lesson comprises two (2) master classes focusing on:

• Simplifying algebraic fractions
• Expanding binomial products
• Expanding and factorising special products
• Factorising algebraic expressions

Content:

MA5-ALG-P-01

Apply the 4 operations involving algebraic fractions with pronumerals in the denominator

• Simplify algebraic fractions, including those involving indices
• Simplify expressions that involve operations with algebraic fractions, including algebraic fractions that involve pronumerals in the denominator and/or indices

Factorise algebraic expressions by taking out a common algebraic factor

• Factorise algebraic expressions, including those involving indices, by determining the highest common factors (HCF) including negative coefficients/pronumerals

Expand binomial products and factorise monic quadratic expressions

• Expand binomial products
• Factorise monic quadratic trinomial expressions
• Solve problems involving expansion and factorisation of algebraic expressions

MA5-ALG-P-02

Operate with algebraic fractions involving binomial numerators and numerical denominators

• Add and subtract algebraic fractions with binomial numerators and numerical denominators

Expand, factorise and simplify algebraic expressions including special products

• Prove and apply these special products \( (a-b)(a+b)=a^2-b^2 \), \( (a+b)^2=a^2+2ab+b^2 \),  \( (a-b)^2=a^2-2ab+b^2 \)
• Expand and simplify a variety of algebraic expressions including binomial products and the special products
• Factorise algebraic expressions involving the special products and strategies, including common factors, grouping in pairs for 4-term expressions and quadratic trinomials (monic and non-monic)
• Simplify algebraic expressions involving algebraic fractions using factorisation