Maths Revision! -Algebra

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  • Created by: Livviemt
  • Created on: 12-03-16 16:32

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 Equation: c^3 times c^2 (http://a.files.bbci.co.uk/equation-chef/live/58b244b173d132e850a095c1d7c91a08/18).

To answer this question, write Equation: c^3 (http://a.files.bbci.co.uk/equation-chef/live/97100d33c3e36453e533f599cfc00135/18) and Equation: c^2 (http://a.files.bbci.co.uk/equation-chef/live/2796af5074a7f27ecccd3cd17e165d53/18) out in full: Equation: c^3 = c times c times c (http://a.files.bbci.co.uk/equation-chef/live/f62b52007b2bac9aecdf662df578fffa/18) andEquation: c^2 = c times c (http://a.files.bbci.co.uk/equation-chef/live/a357274ef7e63ce2758741c7086380ef/18).

Writing the indices out in full shows that Equation: c^3 times c^2 (http://a.files.bbci.co.uk/equation-chef/live/58b244b173d132e850a095c1d7c91a08/18) means Equation: c (http://a.files.bbci.co.uk/equation-chef/live/4a8a08f09d37b73795649038408b5f33/18) has now been multiplied by itself 5 times. This meansEquation: c^3 times c^2 (http://a.files.bbci.co.uk/equation-chef/live/58b244b173d132e850a095c1d7c91a08/18) can be simplified to Equation: c^5 (http://a.files.bbci.co.uk/equation-chef/live/f03070af965b1d3db3c9dc04db25ea96/18).

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(x1)2(3x+4)+4(x−1).

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

2(3x+4)+4(x1)=6x+8+4x4=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 -

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