Solve:
${(4 a + 36)}^{2} - {(4 a - 36)}^{2} + 48 a b$

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Solution

We have,

${(4 a + 36)}^{2} - {(4 a - 36)}^{2} + 48 a b$

$= {(4 a + 36)}^{2} - {(4 a - 36)}^{2} + 48 a b$

$= {(4 a)}^{2} + {(36)}^{2} + 2 \times 4 a \times 36 - [{(4 a)}^{2} + {(36)}^{2} - 2 \times 4 a \times 36] + 48 a b$

$= {(4 a)}^{2} + {(36)}^{2} + 2 \times 4 a \times 36 - {(4 a)}^{2} - {(36)}^{2} + 2 \times 4 a \times 36 + 48 a b$

$= 288 a + 288 a + 48 a b$

$= 576 a + 48 a b$

$= 48 a (12 + b)$

Hence, the answer is $48 a (12 + b)$ .

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