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Expanding and Factorising. Expanding Can’tcannot What is ‘expanding’?

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Text of Expanding and Factorising. Expanding Can’tcannot What is ‘expanding’?

Expanding and Factorising

Expanding and Factorising

Expanding

Cant cannotWhat is expanding?ExpandingYes, that is expanding

But what we want to know is how to expand an algebraic equation

3(7 + 10)5x(6y 7z)4(x 4) + 5ExpandingExpansion means to multiply everything inside the brackets by what is directly outside the brackets

Think WriteWrite the expressionExpand the bracketsMultiply out the brackets4(x 4) + 5= 4(x) + 4(-4) + 5= 4x -16 + 5Expanding single bracketsAfter expanding brackets, simplify by collecting any like termsThinkCollect any like terms= 4x -16 + 5

= 4x - 11WriteYour turn.......

Remember:Stop and thinkAsk your neighbour quietlyHand-upMove on until I can get to youSome music as you work

Got a questionExpanding two bracketsExpand each bracket: working from left to rightExpanding pairs of bracketsWhen multiplying expressions within pairs of brackets, multiply each term in the first bracket by each term in the second bracket, then collect the like termsExpanding pairs of bracketsYou can use the FOIL method to help you keep track of which terms are to be multiplied togetherFirst multiply the first term in each bracketOuter multiply the 2 outer termsInner multiply the 2 inner termsLast multiply the last term of each bracket Expansion patternsDifference of two squares (a + b) (a b) = a2 b2 Expansion patternsPerfect squares (identical brackets) Square the first term, add the square of the last term, then add (or subtract) twice their product (a + b) (a + b) = a2 + 2ab + b2 (a b) (a b) = a2 2ab b2Expanding more than two bracketsBrackets or pairs of brackets that are added or subtracted must be expanded separately

Always collect any like terms following an expansionFactorising Factorising is the opposite of expanding, going from an expanded form to a more compact form

Factor pairs of a term are numbers and pronumerals which, when multiplied together, produce the original termHighest Common FactorThe number itself and 1 are factors of every integer

The highest common factor (HCF) of given terms is the largest factor that divides into all terms without a remainderFactorising using the highest common factorAn expression is factorised by finding the HCF of each term, dividing it into each term and placing the result inside the brackets, with the HCF outside the bracketsFactorising using the difference of two squares ruleTo factorise a difference of two squares, a2 b2 we use the rule or formula (a + b) (a b) = a2 b2 in reverse a2 b2 = (a + b) (a b)Factorising using the Difference-of-two-squares ruleLook for the common factor first If there is one, factorise by taking it out

Rewrite the expression showing the two squares and identifying the a and b parts of the expressionFactorising using the Difference-of-two-squares ruleFactorise, using the rule a2 b2 = (a + b) (a b)Simplifying algebraic fractionsFactorise the numerator and the denominator

Cancel factors where appropriateSimplifying algebraic fractionsIf two fractions are multiplied, factorise where possible then cancel any factors, one from the numerator and one from the denominatorSimplifying algebraic fractionsIf two fractions are divided, remember to multiply the reciprocal of the second fraction before factorising and cancelling

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