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Trinomials of the Form ax² ± bx ± c

Factorise the...

Question

Factorise the following:
$3 a^{2} - 11 a b + 6 b^{2}$

A

(a - 2 b) (a - b)

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B

(3 a + b) (5 a - b)

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C

(a - 2 b) (2 a - 3 b)

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D

(3 a - 2 b) (a - 3 b)

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Solution

The correct option is D $(3 a - 2 b) (a - 3 b)$
$3 a^{2} - 11 a b + 6 b^{2}$
$= 3 a^{2} - 9 a b - 2 a b + 6 b^{2}$
$= 3 a (a - 3 b) - 2 b (a - 3 b)$
$= (a - 3 b) (3 a - 2 b)$

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Similar questions

(3 a + \frac{2}{b}) (2 a - \frac{3}{b})

Q. Prove the following identities:

\sum (b + c - 2 a)^{3} = 3 (b + c - 2 a) (c + a - 2 b) (a + b - 2 c)

2 a + 6 b - 3 (a + 3 b)^{2}

2 a + 6 b - 3 (a + 3 b)^{2}

= 2 (a + 3 b) - 3 (a + 3 b)^{2} [T a k i n g 2 c o m m o n f r o m 2 a + 6 b]

= (a + 3 b) {\begin{matrix} 2 - 3 (a + 3 b) \end{matrix}} [T a k i n g (a + 3 b) c o m m o n]

= (a + 3 b) (2 - 3 a - 9 b)

a^{2} - a b - 3 a + 3 b

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