03Fsumof2cubes

= Sum and Difference of Two Cubes =

We have two rules for factorising cubics

... ... ** a 3 + b 3 = ( a + b )( a 2 – ab + b 2 ) **

... ... ** a 3 – b 3 = ( a – b )( a 2 + ab + b 2 ) **


 * You can confirm that these are correct by expanding the brackets on the right.
 * Notice that the sign in the left side is matched by the sign in the first bracket on the right.


 * Example 1 **

... ... Factorise x 3 – 27


 * Solution:**

math \\ . \qquad x^3 - 27 \\. \\ . \qquad = x^3 - 3^3 \qquad \{ \textit{this is a difference of two cubes} \} \\. \\ . \qquad = \big( x - 3 \big) \big( x^2 + 3x + 9 \big) math


 * Example 2 **

... ... Factorise 3(x + 1) 3 + 24


 * Solution:**

math \\ . \qquad 3 \big( x + 1 \big)^3 + 24 \qquad \{ \textit{take out 3 as a common factor} \} \\. \\ . \qquad = 3 \Big( \big( x + 1 \big)^3 + 8 \Big) \\. \\ . \qquad = 3 \Big( \big( x + 1 \big)^3 + 2^3 \Big) \qquad \{ \textit{this is a sum of two cubes} \} \\. \\ . \qquad = 3 \big( x + 1 + 2 \big) \Big( \big(x + 1 \big)^2 - 2 \big( x + 1 \big) + 2^2 \Big) \\. \\ . \qquad = 3 \big( x + 3 \big) \big( x^2 + 2x + 1 - 2x - 2 + 4 \big) \\. \\ . \qquad = 3 \big( x + 3 \big) \big( x^2 + 3 \big) math


 * Factorising With the ClassPad Calculator **
 * Your calculator can factorise cubics like these.


 * The factor command is in the ACTION menu, TRANSFORMATION submenu.

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