Simplify: $x (x - 3)^{2} + 2$ and find the value of the expression at $x = 1$ .

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Solution

$x (x - 3)^{2} + 2$

$= x [x^{2} + 9 - 6 x] + 2$

$= x^{3} + 9 x - 6 x^{2} + 2$

$= x^{3} - 6 x^{2} + 9 x + 2$

Put $x = 1$

$= (1)^{3} - 6 (1)^{2} + 9 (1) + 2$

$= 1 - 6 + 11$

$= 12 - 6$

$= 6$ .

$∴ x (x - 3)^{2} + 2 = 6$ .

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