Gr 9 (Algebra)

Summary of Algebraic Expressions

Algebraic Language:

algebraic expressions. Monmials, binomials, and trinomials.

Expand and Simplify Expressions:

Apply laws of exponents for simplification. Multiply  and divide integers and polynomials

Add and subtract like terms

Operations with Fractions:

Include common and decimal fractions in calculations with algebraic expressions.

Factorization:

Factorize algebraic expressions involving common factors, difference of squares, and trinomials 

Simplify expressions using factorization.

Summary of Algebraic Equations

set up equations to describe problem situations  Solve equations by inspection

 use additive and multiplicative inverses Use laws of exponents -  

Solve equations by substitution Equations with factorisation    (x + a)(x + b) = 0

Summary of Algebraic Expressions

Algebraic Language:

• Understand conventions for writing algebraic expressions. - Identify and classify like and unlike terms.

• Recognize coefficients (numerical factors) and exponents (powers). - Distinguish monomials, binomials, and trinomials.

Expand and Simplify Expressions:

• Use commutative, associative, and distributive laws to manipulate expressions.

• Apply laws of exponents for simplification. - Add and subtract like terms.

• Multiply integers and polynomials - Divide polynomials and trinomials by integers or monomials.

• Simplify expressions - Determine squares, cubes, square roots, and cube roots of algebraic terms.

Operations with Fractions:

• Include common and decimal fractions in calculations with algebraic expressions.

Advanced Algebraic Manipulations:

• Multiply integers and monomials by polynomials. - Divide polynomials by integers or monomials.

• Expand and simplify the product of two binomials and the square of a binomial.

Factorization:

• Factorize algebraic expressions involving common factors, difference of squares, and trinomials 

• Simplify expressions using factorization. - Use factorization to simplify algebraic fractions.

Summary of Algebraic Equations

• set up equations to describe problem situations  - analyse and interpret equations 

• Solve equations by inspection - use additive and multiplicative inverses

•  use laws of exponents -  Solve equations by substitution

• Extend solving equations to include: - factorisation    - equations of the form: a product of factors = 0