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# Factorising algebraic expressions

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A slideshow to explain the process of factorising algebraic expressions.

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### Factorising algebraic expressions

1. 1. Factorising Algebraic Expressions<br />
2. 2. This is factorising…<br />8<br /> <br />=4×2<br /> <br />=8×1<br /> <br />6𝑎<br /> <br />=6×𝑎<br /> <br />=6𝑎×1<br /> <br />𝑚2<br /> <br />=𝑚×𝑚<br /> <br />12𝑦2<br /> <br />=3×4𝑦2<br /> <br />=4𝑦×3𝑦<br /> <br />
3. 3. This is an algebraic expression:<br />2𝑎+6<br /> <br />Algebraic expressions can sometimes be factorised.<br />2×(𝑎+3)<br /> <br />=<br /> <br />2𝑎+6<br /> <br />=<br /> <br />2(𝑎+3)<br /> <br />
4. 4. 𝑎<br /> <br />𝑎<br /> <br />6<br /> <br />+<br /> <br />2𝑎<br /> <br />
5. 5. 𝑎+3<br /> <br />𝑎+3<br /> <br />2×(𝑎+3)<br /> <br />2(𝑎+3)<br /> <br />Factorised algebraic expression<br />
6. 6. 2𝑎+6<br /> <br />Factors of  𝟐𝒂<br /> <br />Factors of  𝟔<br /> <br />3, 2, 1, 6<br /> <br />2, 1, 𝑎<br /> <br />𝐻𝐶𝐹=2<br /> <br />=2×𝑎<br /> <br />+ 2×3<br /> <br />2𝑎+6<br /> <br />=2×(𝑎+3)<br /> <br />=2(𝑎+3)<br /> <br />
7. 7. 8𝑚+12<br /> <br />Factors of  𝟖𝒎<br /> <br />Factors of  𝟏𝟐<br /> <br />3, 4, 2, 6, 1, 12<br /> <br />1, 8, 2, 4, 𝑚<br /> <br />𝐻𝐶𝐹=4<br /> <br />+ 4×3<br /> <br />=4×2𝑚<br /> <br />8𝑚+12<br /> <br />=4×(2𝑚+3)<br /> <br />=4(2𝑚+3)<br /> <br />
8. 8. 5𝑎𝑏+10𝑎<br /> <br />Factors of  𝟓𝒂𝒃<br /> <br />Factors of  𝟏𝟎𝒂<br /> <br />2, 5, 1, 10, 𝑎<br /> <br />1, 5, 𝑎, 𝑏<br /> <br />𝐻𝐶𝐹=5𝑎<br /> <br />+ 5𝑎×2<br /> <br />=5𝑎×𝑏<br /> <br />5𝑎𝑏+10𝑎<br /> <br />=5𝑎×(𝑏+2)<br /> <br />=5𝑎(𝑏+2)<br /> <br />
9. 9. 9𝑗𝑘+4𝑘<br /> <br />Factors of  𝟗𝒋𝒌<br /> <br />Factors of  𝟒𝒌<br /> <br />1, 4, 𝑘<br /> <br />1, 9, 𝑗, 𝑘<br /> <br />𝐻𝐶𝐹=𝑘<br /> <br />+ 𝑘×4<br /> <br />=𝑘×9𝑗<br /> <br />9𝑗𝑘+4𝑘<br /> <br />=𝑘×(9𝑗+4)<br /> <br />=𝑘(9𝑗+4)<br /> <br />
10. 10. 𝐻𝐶𝐹=3<br /> <br />12h+3<br /> <br />=3×4h+3×1<br /> <br />+<br /> <br />=3(4h+1)<br /> <br />4h<br /> <br />1<br /> <br />𝐻𝐶𝐹=𝑏<br /> <br />𝑎𝑏−4𝑏<br /> <br />=𝑏×𝑎−𝑏×4<br /> <br />=𝑏(𝑎−4)<br /> <br />𝑎<br /> <br />4<br /> <br />−<br /> <br />