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Algebra The Basics


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Algebra, level 2 in the UK system. One pdf slide with an A4 format handout that summarises collecting terms, multiplying terms, cancelling algebraic fractions, multiplying out brackets.

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Algebra The Basics

  1. 1. Simplifying expressions Collecting terms Multiplying terms Dividing terms Multiply out brackets Remember Remember BODMAS says 3 47=3×11=33 You can divide powers of Y × X = YX • • • ­3x the same number by You can also do the sum like this P × P = P2 • subtracting the powers, so 3 47=3×43×7=33 58 2 • –4 × 5 = –20 • =5 Remember that a 'term' has a 6 5 So, look at the lines... –7 × –9 = +63 • sign, a number and a letter. The −12 −3 3 2 x4=3×2 x3×4=6 x12 sign stays 'glued' onto the number So = The rules are • 8 2 and letter so you can move them 2y = –6xy × ­3x the same as for multiplying around... Try to follow these examples (and remember your directed numbers) E.G. 1. So 5x3y−3x2y is the The steps The steps same as 5x−3x3y2y 1. Sort out the signs because I just moved the -3x. This 1. Sort out the signs 2. Multiply the numbers 23x −5=6x −10 1. works out to be 2x5y 2. Cancel the numbers 3. Multiply the letters 2. −32x −1=−6x 3 3. Work out the powers of the E.G. 2. Sometimes you have to 3. −5 3−2x =−1510x Some examples letters think about the directed numbers, 4. −2y 3x4 =−6xy−8y so 7x−4y−3x−6y is the same A few examples 1. −4r×3q=−12rq as 7x−3x−4y−6y=4x−10y 15xy 2. −6x×8y=−48xy 1. =3y Xs cancelled A minus sign outside the bracket 5x E.G. 3. Powers must be treated x× x×x× x=x 4 3. simply switches all the signs in as different symbols, so in the 12x2 y 2 4 the bracket. 2. = xy 2 4. 3×r×r×h=3 r h expression 5p2 −3p−2p2 7p , 9xy 3 If there are two brackets, just you treat p2 as different to p, 2x×−3y×12x=−72 x 2 y 5. 21 p q3 3 giving 3. = 1. Multiply out the first Make sure you know how the 23 14 p q 2 p 2 2 2 5p −2p 7p−3p=3p −4p examples work, and then try the 2. Multiply out the second Your turn, try cancelling the ones on the practice sheet before Try the ones on the practice sheet 3. Collect the terms! algebraic fractions on the practice moving on... now before moving on... sheet... Your turn... KPB 2009