Factorise :
27−x3y3+6−2xy27 - x^3y^3 + 6 - 2xy27−x3y3+6−2xy
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27−x3y3+6−2xy=(33−(xy)3)+(6−2xy)=(3−xy)(32+3xy+(xy)2)+2(3−xy)=(3−xy)(32+3xy+x2y2)+2(3−xy)=(3−xy)((9+3xy+x2y2)+2)=(3−xy)(9+3xy+x2y2+2)=(3−xy)(11+3xy+x2y2)27 - x^3y^3 + 6 - 2xy = (3^3 - (xy)^3) + (6 - 2xy)\\[1em] = (3 - xy)(3^2 + 3xy + (xy)^2) + 2(3 - xy)\\[1em] = (3 - xy)(3^2 + 3xy + x^2y^2) + 2(3 - xy)\\[1em] = (3 - xy)\Big((9 + 3xy + x^2y^2) + 2\Big)\\[1em] = (3 - xy)\Big(9 + 3xy + x^2y^2 + 2\Big)\\[1em] = (3 - xy)(11 + 3xy + x^2y^2)27−x3y3+6−2xy=(33−(xy)3)+(6−2xy)=(3−xy)(32+3xy+(xy)2)+2(3−xy)=(3−xy)(32+3xy+x2y2)+2(3−xy)=(3−xy)((9+3xy+x2y2)+2)=(3−xy)(9+3xy+x2y2+2)=(3−xy)(11+3xy+x2y2)
Hence, 27−x3y3+6−2xy=(3−xy)(11+3xy+x2y2)27 - x^3y^3 + 6 - 2xy = (3 - xy)(11 + 3xy + x^2y^2)27−x3y3+6−2xy=(3−xy)(11+3xy+x2y2).
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