Find the value of $2 a^{2} - 3 b^{2} + 4 c^{2} - 5 d^{2}$ when $a = 3, b = 0, c = 2$ and $d = 1$

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Solution

By substituting the value of $a = 3, b = 0, c = 2$ and $d = 1$ in $2 a^{2} - 3 b^{2} + 4 c^{2} - 5 d^{2}$ we get
$2 a^{2} - 3 b^{2} + 4 c^{2} - 5 d^{2}$
$= 2 {(3)}^{2} - 3 {(0)}^{2} + 4 {(2)}^{2} - 5 {(1)}^{2}$
$= 2 \times 9 - 3 \times 0 + 4 \times 4 - 5 \times 1$
$= 18 - 0 + 16 - 5$
$= 34 - 5 = 29$

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