Manipulation of Formulae and Expressions

Manipulation of Formulae and Expressions

Understanding and Recognising Expressions

• Algebraic expressions can consist of variables, constants, and operations.
• Variables can represent any numbers, and their values are generally unknown.
• Constants are fixed numbers and do not change.
• The value of an expression can change based on the given values for the variables.

Simplifying Expressions

• Combining like terms is the process of adding or subtracting terms with the same variables and powers.
• Keep in mind the order of operations (parentheses, exponents, multiplication and division, addition and subtraction - PEMDAS) when simplifying expressions.
• Distributing, or multiplying a value through parenthesis, can help break down complex expressions.

Factoring Expressions

• Factoring involves breaking down an expression into its smallest inseparable pieces, called factors.
• Common factor is a number, variable or expression which evenly divides two or more monomials.
• Difference of squares is a special pattern that occurs in algebra where a^2 - b^2 = (a+b)(a-b).

Rational Expressions

• Rational expressions are fractions where the numerator and the denominator are polynomials.
• These expressions can be simplified by finding common factors in the numerator and the denominator and dividing them out.

Working with Formulas

• A formula is an equation that describes a relationship between quantities.
• Formulas can be rearranged to solve for different variables.
• To manipulate a formula means to rewrite it in terms of another variable.

The ability to manipulate expressions and formulas is central to algebra. This skill will be important in tackling more complex topics in the subject.