Fatorise:
$9 - (a^{2} + 2 a b - b^{2})$

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Solution

$9 - (a^{2} - 2 a b + b^{2}) [∵ (a - b)^{2} = a^{2} - 2 a b + b^{2}]$

$\Rightarrow 9 - (a - b)^{2} = (3)^{2} - (a - b)^{2}$

$\Rightarrow (3 - a + b) (3 + a - b)$ $[∵ a^{2} - b^{2} = (a + b) (a - b)]$

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\sqrt{\frac{a^{2} + 2 a b + b^{2}}{a^{2} - 2 a b + b^{2}}}

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How can we factorise a²+ 2ab + b²-9

(a - b)^{2} = a^{2} + 2 a b - b^{2}

(a - b)^{2} = a^{2} - 2 a b + b^{2}

(a - b)^{2} = a^{2} - b^{2}

(a + b)^{2} = a^{2} + 2 a b - b^{2}

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