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Question Number 216183 by MATHEMATICSAM last updated on 29/Jan/25

Answered by A5T last updated on 29/Jan/25

$$={\mathrm{a}}^3-{\mathrm{a}}^2(\mathrm{b}+\mathrm{c})+{\mathrm{b}}^3+{\mathrm{c}}^3+2\mathrm{abc}-{\mathrm{b}}^2(\mathrm{a}+\mathrm{c})-{\mathrm{c}}^2(\mathrm{a}+\mathrm{b})$$$$={\mathrm{a}}^2(\mathrm{a}-\mathrm{b}-\mathrm{c})+{\mathrm{b}}^3+{\mathrm{c}}^3+2\mathrm{bc}(\mathrm{a}-\mathrm{b}-\mathrm{c}+\mathrm{b}+\mathrm{c})$$$$-{\mathrm{b}}^2(\mathrm{a}-\mathrm{b}-\mathrm{c}+\mathrm{b}+2\mathrm{c})-{\mathrm{c}}^2(\mathrm{a}-\mathrm{b}-\mathrm{c}+2\mathrm{b}+\mathrm{c})$$$$=(\mathrm{a}-\mathrm{b}-\mathrm{c})({\mathrm{a}}^2+2\mathrm{bc}-{\mathrm{b}}^2-{\mathrm{c}}^2)$$$$=(\mathrm{a}-\mathrm{b}-\mathrm{c})(\mathrm{a}-\mathrm{b}+\mathrm{c})(\mathrm{a}+\mathrm{b}-\mathrm{c})$$

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