Which of the following expression(s) is/are incorrect?

{(x - 4)}^{2} = (x - 4) (x - 4)

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x^{2} - 8 x + 16 = (x - 4) (x - 4)

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x^{2} - 4 x + 16 = (x - 4) (x - 4)

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x^{2} - 18 x - 16 + 10 x = (x - 4) (x - 4)

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Solution

The correct options are
C $x^{2} - 18 x - 16 + 10 x = (x - 4) (x - 4)$
D $x^{2} - 4 x + 16 = (x - 4) (x - 4)$
Option C : $R H S = (x - 4) (x - 4)$
$= x (x - 4) - 4 (x - 4)$
$= x^{2} - 4 x - 4 x + 16$
$= x^{2} - 8 x + 16$
$\neq L H S$

Option D : $R H S = (x - 4) (x - 4)$
$= x (x - 4) - 4 (x - 4)$
$= x^{2} - 4 x - 4 x + 16$
$= x^{2} - 8 x + 16$ ....(1)
$L H S = x^{2} - 18 x - 16 + 10 x$
$= x^{2} - 8 x - 16$ ...(2)
$∴ L H S \neq R H S$ ...From (1) & (2)

$∴$ both options C and D are incorrect.

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