# Products and Factors

### Year 10 Maths: Chapter 5

## In this chapter you will learn to:

- The index laws
- Fractional indices
- Adding and subtracting algebraic fractions
- Multiplying and dividing algebraic fractions
- Expanding and factorising expressions
- Expanding binomial products
- Factorising special binomial products
- Factorising quadratic expressions

## 1. The index laws

Write these out on a piece of paper and

**memorise them!!!**Exponent rules part 1 | Exponents, radicals, and scientific notation | Pre-Algebra | Khan Academy

## 2. Fractional indices

We use fractional indices to work with square, cubes and further roots

Zero, negative, and fractional exponents | Pre-Algebra | Khan Academy

## 3. Adding and subtracting algebraic fractions

To

**add or subtract fractions**convert them (if needed) so they have the same denominator and then add or subtract the numerators*See examples on p. 161*

Algebraic expression adding fractions | Introduction to algebra | Algebra I | Khan Academy

## 4. Multiplying and dividing algebraic fractions

- To
**multiply fractions,**cancel any common factors and multiply the numerator and denominator separately - To
**divide by a fraction (e.g. a/b)**, multiply by its*reciprocal*(b/a)

Algebraic expressions with fraction division | Introduction to algebra | Algebra I | Khan Academy

## 5. Expanding and Factorising Algebraic Expressions

Expanding and factorising are inverse operations.

When 4(2a + 5) is **expanded**, the answer is 8a + 20

When 8a + 20 is **factorised, ** the answer is 4(a+5)

__Summary: Expanding an Expression__

Multiply each term inside the brackets by the term outside the brackets:

**a(b + c) = ab + bc**

**a(b - c) = ab - ac**

__Summary: Factorising an expression__

- Divide the HSC of the terms and write it outside the brackets
- Divide each term b the HSC and write the answers inside the brackets:

**ab + ac = a(b + c)**

**ab - ac = a(b - c)**

- To check that the factorised answer is correct, expand it

Algebra - expanding and simplifying brackets

## 6. Expanding binomial products

(a + 3) and (x-2) are called

**binomial expressions**because each expression expression has exactly two terms (binomial means 'two terms').(a + 3)(x - 2) is called a **binomial product** because it is a product (multiplication) of two binomial expressions

Algebra - expanding brackets - binomials

## Perfect squares

Algebra - Perfect Square Factoring and Square Root Property

## Difference of two squares

Factor the Difference of Two Squares

## 8. Factorising quadratic expressions

- A quadratic expression is an algebraic expression where the highest power of the variable is '2'.
- Such an expression is called a 'trinomial' because it has three terms

To factorise such terms:

- Find two numbers that have a sum of
*b*and a product of*c*. - Use these two numbers to write a binomial product in the form (x ____)(x_____)

❤² How to Solve Quadratic Equations By Factoring (mathbff)