Square root of the expression $16 a^{2} + 9 b^{2} - 24 a b + 24 a - 18 b + 9$ is . (2 marks)

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Solution

$\sqrt{16 a^{2} + 9 b^{2} - 24 a b + 24 a - 18 b + 9}$
= $\sqrt{(4 a)^{2} + (3 b)^{2} + (3)^{2} + 2 (4 a) (- 3 b) + 2 (- 3 b) (3) + 2 (4 a) (3)}$
= $\sqrt{(4 a - 3 b + 3)^{2}}$
= $| 4 a - 3 b + 3 |$ (2 marks)

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16 a^{2} + 9 b^{2} - 24 a b + 24 a - 18 b + 9

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