Question

Subtract $3\mathrm{l}(\mathrm{l}-4\mathrm{m}+5\mathrm{n})$ from $4\mathrm{l}(10\mathrm{n}-3\mathrm{m}+2\mathrm{l})$.

Answer 1

Algebric subtraction:

We have to subtract $3\mathrm{l}(\mathrm{l}-4\mathrm{m}+5\mathrm{n})$ from $4\mathrm{l}(10\mathrm{n}-3\mathrm{m}+2\mathrm{l})$.

$$\begin{gathered} 4\mathrm{l}\left(10\mathrm{n}-3\mathrm{m}+2\mathrm{l}\right)-3\mathrm{l}\left(\mathrm{l}-4\mathrm{m}+5\mathrm{n}\right) \\ =\left(40\ln -12\mathrm{lm}+8{\mathrm{l}}^2\right)-\left(3{\mathrm{l}}^2-12\mathrm{lm}+15\ln \right) \\ =40\ln -12\mathrm{lm}+8{\mathrm{l}}^2-3{\mathrm{l}}^2+12\mathrm{lm}-15\ln \\ =8{\mathrm{l}}^2-3{\mathrm{l}}^2+12\mathrm{lm}-12\mathrm{lm}+40\ln -15\ln \\ =5{\mathrm{l}}^2+25\ln \end{gathered}$$

Therefore, the required answer is $\mathbf{5}{\mathbf{l}}^{\mathbf{2}}\mathbf{+}\mathbf{25}\mathit{l}\mathit{n}$.