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Introducing algebra<br />BTEOTSSSBAT simplify equations and use substitution<br />
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In algebra:<br />x + 2 means two more than x<br />x – 3 means three less than x<br />x + y means add together x and y<br />3x means three times x. We don’t usually use a multiplication sign! So 3x = 3 x<br /> means x divided by four. <br />We can also write this as x 4<br />x² means x multiplied by itself: x x<br />
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Write down the algebraic expression that means:<br />3 more than y<br />5 less than s<br />x divided by y<br />w multiplied by 4<br />f multiplied by 3 and divided by t<br />4 less than x multiplied by 4 <br />
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Simplifying (collecting like terms)<br />To simplify an algebraic expression we have to collect like terms; only like terms can be added or subtracted<br />For example<br />2a + 4a = 6a<br />but 2a + 7b can’t be made any simpler.<br />
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Simplify these expressions<br />(a) a + a + a<br />(b) b + b + b – b<br />(c) 3a + 2a<br />(d) 3a + 2b – a<br />
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Brackets<br />Sometimes brackets are used in expressions e.g. 3 (x + 4)<br />A number next to a bracket multiplies everything inside the bracket.<br />So, 3 (x + 4) is the same as 3 (x + 4) = <br /> 3 x + 3 4<br />This can be simplified to 3x + 12.<br />
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Example<br />Expand 3(2x + 5)<br />Here the 3 multiplies the 2x as well as the 5<br />This gives 3 × 2x + 3 × 5 = 6x + 15.<br />
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Multiply out the brackets and if necessary simplify the expression<br />(a) 2 (x+3)<br />(b) 4 (x + 4)<br />(c) 5 (2x + 5)<br />
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Substitution<br />Substituting in a formula means replacing the letters by numbers<br />For example, in the formula A = lw<br />If l = 3 and w = 4 <br />Then lw = 3 4 = 12<br />
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Other examples:<br />If a = 3 and b = 4, what is the value of a + b?<br />Using substitution, a + b = 3 + 4 = 7<br />(ii) If a = 5, what is the value of 4a?<br />Using substitution, 4a = 4 5 = 20<br />(iii) If x = 6 and y = 5, what is the value of 2xy?<br />Using substitution, xy = x y = 6 5 = 30<br /> and 2xy = 2 x y = 2 6 5 = 60<br />
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When a = 7, b = 4, x = 2 and y = 5, work out the values of<br />a)a + b + y b) ax c) by <br />3a – 4 e) bx + 2 f) 3xy<br />3x + y h) 2b – x i) 2ax + 3y<br />j) ab – x k) ay + bxl) 2axy<br />
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