Question

From the sum of a2 + 3b2 - 5c2 and 8a2 + 15b2 - 14c2 subtract the sum of 7a2 - 2b2 + 5c2 and 4a2 - 3b2 + 2c2.​

Answer 1

Answer:

$\tt{SOLUTION:-}$

$\implies \tt \purple{ {a}^{2} + {3b}^{2} - {5c}^{2} + {8a}^{2} + {15b}^{2} - {14c}^{2} }$

$\mathtt{ADD \: ALL \: LIKE \: TERMS}$

$\implies \tt \purple{ {a}^{2} + {8a}^{2} + {3b}^{2} + {15b}^{2} - {5c}^{2} - {14c}^{2} + {15b}^{2} }$

$\implies \tt \purple{ {9a}^{2} + {18b}^{2} - {19c}^{2}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt{NOW, ADD \: OTHER \: ONES}$

$\implies \tt \purple{ {7a}^{2} - {2b}^{2} + {5c}^{2} + {4a}^{2} - {3b}^{2} + {2c}^{2} }$

$\implies \tt \purple{ {7a}^{2} + {4a}^{2} - {2b}^{2} - {3b}^{2} + {5c}^{2} + {2c}^{2} }$

$\implies \tt \purple{ {11a}^{2} - {5b}^{2} + {7c}^{2} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\mathtt{NOW \: SUBTRACT}$

$\implies \tt \purple{ {9a}^{2} + {18b}^{2} - {19c}^{2} - (11 {a}^{2} - {5b}^{2} + {7c}^{2}) }$

$\implies \tt \purple{ {9a}^{2} + {18b}^{2} - {19c}^{2} - 11 {a}^{2} + {5b}^{2} - {7c}^{2}) }$

$\implies \tt \purple{ {9a}^{2} - 11 {a}^{2} + {18b}^{2} + {5b}^{2} - {19c}^{2} - {7c}^{2} }$

$\implies \tt \purple{ { - 3a}^{2} + {23b}^{2} - {26c}^{2} }$