1.

Factories 216+27b^3+8c^3_108bc

Answer»

Step-by-step EXPLANATION:

= 216 + {27b}^{3} + {8c}^{3} - 108bc \\ = {(6)}^{3} + {(3b)}^{3} + {(2c)}^{3} - 3 \times 6 \times (3b) \times (2c) \\ \\ we \: know \: that \\ = {a}^{3} + {b}^{3} + {c}^{3} - 3abc \\ where \: \\ a = 6 \\ b = 3b \\ c = 2c \\ = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca \\ \\ = (6 + 3b + 2c)( {6}^{2} + {(3b)}^{2} + {(2c)}^{2} -6 \times 3b - 3 b\times 2c - 2c \times 6 ) \\ = (6 + 3b + 2c)(36 + 9 {b}^{2} + 4 {c}^{2} - 18b - 6bc - 12c )

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