Factorise: $3 a^{2} b c + 6 a b^{2} c + 9 a b c^{2}$

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Solution

Let us first find the HCF of all the terms of the given polynomial $3 a^{2} b c + 6 a b^{2} c + 9 a b c^{2}$ by factoring the terms as follows:

$3 a^{2} b c = 3 \times a \times a \times b \times c 6 a b^{2} c = 3 \times 2 \times a \times b \times b \times c 9 a b c^{2} = 3 \times 3 \times a \times b \times c \times c$

Therefore, $H C F = 3 \times a \times b \times c = 3 a b c$

Now, we factor out the HCF from each term of the polynomial $3 a^{2} b c + 6 a b^{2} c + 9 a b c^{2}$ as shown below:

$3 a^{2} b c + 6 a b^{2} c + 9 a b c^{2} = 3 a b c (a + 2 b + 3 c)$

Hence, $3 a^{2} b c + 6 a b^{2} c + 9 a b c^{2} = 3 a b c (a + 2 b + 3 c)$ .

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