Unit 2: Algebra

 Use the rules of indices to simplify algebraic expressions

An index number, or a power, is the small floating number that goes next to a number or letter. The plural of index number is indices. Index numbersshow how many times a number or letter has been multiplied by itself.

Multiplying Indicies

Simplify .

To answer this question, write  and  out in full:  and.

Writing the indices out in full shows that  means  has now been multiplied by itself 5 times. This means can be simplified to .

Dividing Indicies

 Expand brackets.

Expanding brackets involves removing the brackets from an expression by multiplying out the brackets.

Example 1 - Expanding a single pair of brackets

a) Expand: 3(x+6)3(x+6).

a) Remember to multiply every term inside the brackets by the term outside:

3(x+6)=3×x+3×6=3x+18

Example 2 - Expanding and simplifying brackets

a) Expand and simplify 2(3x+4)+4(x−1)2(3x+4)+4(x−1).

Multiply each bracket out first, then collect the like terms:

2(3x+4)+4(x−1)=6x+8+4x−4=10x+4

Example 3 - Expanding double brackets

Expand and simplify (a+b)(c+d)(a+b)(c+d).

When multiplying out double brackets, each terms in the first bracket must be multiplied by each term in the second:

(a+b)(c+d)=ac+ad+bc+bd(a+b)(c+d)=ac+ad+bc+bd.

Example 4 - Expanding and simplifying quadratic expressions

a) Expand and simplify (x+4)(x+3)(x+4)(x+3).

When multiplying xx by another xx you will end up with an x2x2 term:

(x+4)(x+3)=x2+3x+4x+12=x2+7x+12

 Factorise algebraic expressions.

Factorise the expression: c²- 3c - 10

Write down the expression: c²- 3c - 10

Remember that to factorise an expression we need to look for common factor pairs. In this example we are looking for two numbers that:

• multiply to give -10
• add to give -3

Think of all the factor pairs of -10:

• 1 and -10
• -1 and 10
• 2 and -5
• -2 and 5

Which of these factor pairs can be added to get -3?

Only 2 + (-5) = -3

So the answer is:

c² - 3c - 10 = (c + 2)(c - 5)

Factorising the difference of two squares

Factorise: x² - 4

x² - 4 = (x + 2)(x – 2)

Factorise: x² -…