Using the factorisation of $x y^{2} - x z^{2}$ , evaluate the value of $6 \times 3^{2} - 6 \times 2^{2}$ .

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Solution

The correct option is A
30

$x y^{2} - x z^{2}$
$= x (y^{2} - z^{2})$ (taking $x$ common)
$= x (y + z) (y - z)$
$[∵ a^{2} - b^{2} = (a + b) (a - b)]$

Comparing $6 \times 3^{2} - 6 \times 2^{2}$ with the above, we must have,
$6 \times 3^{2} - 6 \times 2^{2}$
$= 6 (3 + 2) (3 - 2)$
$= (6) (5) (1) = 30$

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1

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Using factor theorem factorise the expression completely: 3³ + 2² – 19 + 6

{sin}^{- 1} (sin \frac{5 π}{6}) + {tan}^{- 1} (tan \frac{5 π}{6})

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