Factorise: ax3y + bx2y3 + cx2yz from Mathematics Factorisation

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139.

Factorise: ax3y + bx2y3 + cx2yz


We have    ax3y2 = a × x × x × x × y × y

               bx2y3 = b × x × x × y × y × y
               
               cx2y2z = c × x × x y × y × z

Obviously,   straight x squared straight y squared is a common factor.

∴  We get                ax3y2 = x2y2 × a × x
                            bx2y3 = x2y2 × b × y
                            cx2y2z = x2y2 × c × z

rightwards double arrow ax3y2 + bx2y3 + cx2y2z = [(x2y2 × a × x) + (x2y2 × b × y) + (x2y2 × c × z)]

                                      = x2y2 [(a × x) + (b × y) + (c × z)]

                                      = x2y2(ax + by + cz)
                              
                          




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