if a+b=10 then the value of a^3+b^3+30ab is

Dear Student,

Please find below the solution to the asked query :

$$\begin{gathered} \mathrm{We} \mathrm{have}, \\ \mathrm{a} + \mathrm{b} = 10 \\ \Rightarrow {\left(\mathrm{a}+\mathrm{b}\right)}^3 = {10}^3 \\ \Rightarrow {\mathrm{a}}^3 + {\mathrm{b}}^3 + 3\mathrm{ab}\left(\mathrm{a}+\mathrm{b}\right) = 1000 \\ \Rightarrow {\mathrm{a}}^3 + {\mathrm{b}}^3 + 3\mathrm{ab} \times 10 = 1000 \\ \Rightarrow {\mathrm{a}}^3 + {\mathrm{b}}^3 + 30\mathrm{ab} = 1000 \end{gathered}$$

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