Factorise : $x^{3} - 12 x^{2} + 36 x$

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Solution

Given: $x^{3} - 12 x^{2} + 36 x$
$= x (x^{2} - 12 x + 36)$ , ---------(take $x$ common)
$= x (x^{2} - 2 \times 6 \times x + 6^{2})$ 9Since, $a^{2} - 2 a b + b^{2} = (a - b)^{2}$ )
$= x (x - 6)^{2}$

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x^{3} + 12 x^{2} - 31 x - 42

x^{3} - 12 x^{2} + 36 x + 17

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f (x) = x^{3} + 12 x^{2} + 36 x + 6

Factorise:

(i) x² + 14x + 49; (ii) 4x² + 4x + 1; (iii) a² − 10a + 25; (iv) 2x² − 24x + 72;

(v) p² − 24p + 144; (vi) x³ − 12x² + 36x.

Factorise :

$12 x^{2} - 27$

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