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Factorisation by Common Factors

vii Factorise...

Question

Question 2(vii)
Factorise the following expressions
$10 a^{2} - 15 b^{2} + 20 c^{2}$

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Solution

$10 a^{2} = 2 \times 5 \times a \times a 15 b^{2} = 3 \times 5 \times b \times b 20 c^{2} = 2 \times 2 \times 5 \times c \times c T h e c o m m o n f a c t o r i s 5 10 a^{2} - 15 b^{2} + 20 c^{2} = (2 \times 5 \times a \times a) - (3 \times 5 \times b \times b) + (2 \times 2 \times 5 \times c \times c) = 5 [(2 \times a \times a) - (3 \times b \times b) + (2 \times 2 \times c \times c)] = 5 (2 a^{2} - 3 b^{2} + 4 c^{2})$

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10 a^{2} - 15 b^{2} + 20 c^{2}

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