Question

30. Without actually calculating the cubes, find the values of :-
$1){\left(27\right)}^3+{\left(-17\right)}^3+{\left(-10\right)}^{3}2){\left(-28\right)}^3+{\left(15\right)}^3+{\left(13\right)}^3.$

31. Using suitable identity, find the value of :
$\frac{86\times 86\times 86+14\times 14\times 14}{86\times 86-86\times 14+14\times 14}.$

Answer 1

Dear student
$$\begin{gathered} 31. \\ \frac{86\times 86\times 86+14\times 14\times 14}{86\times 86-86\times 14+14\times 14} \\ =\frac{{86}^3+{14}^3}{{86}^2-86\times 14+{14}^2} \\ =\frac{\left(86+14\right)\left(\cancel{{86}^2+{14}^2-86\times 14}\right)}{\cancel{{86}^2-86\times 14+{14}^2}} \\ =100 \\ \mathrm{Note}: \\ {\mathrm{a}}^3+{\mathrm{b}}^3=\left(\mathrm{a}+\mathrm{b}\right)\left({\mathrm{a}}^2+{\mathrm{b}}^2-\mathrm{ab}\right) \end{gathered}$$
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