9a2+24ab+16b2=32a2+24ab+42b2=(3a)2+2×3×4×a×b+(4b)2=(3a+4b)2=(3a+4b)(3a+4b)

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$9 a^{2} + 24 a b + 16 b^{2} =$

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$3 a + 4 b$

$3 a - 4 b$

$4 a - 3 b$

$4 a + 3 b$

answer is A.

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Detailed Solution

$\begin{array}{l} 9 a^{2} + 24 a b + 16 b^{2} \\ = 3^{2} a^{2} + 24 a b + 4^{2} b^{2} \\ = {(3 a)}^{2} + 2 \times 3 \times 4 \times a \times b + {(4 b)}^{2} \\ = {(3 a + 4 b)}^{2} \\ = (3 a + 4 b) (3 a + 4 b) \end{array}$

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