Using the identity a^2 b^2=(a+b)(a b) By using the above identity, the equation 100 9x^2 #160;can be factorised as follows: 100 9x^2=(10)^2 (3x ...

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Factorisation Using Algebraic Identities

Factorise: ...

Question

Factorise: $100 - 9 x^{2}$

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Solution

Using the identity $a^{2} - b^{2} = (a + b) (a - b)$

By using the above identity, the equation $100 - 9 x^{2}$ can be factorised as follows:

$100 - 9 x^{2} = (10)^{2} - (3 x)^{2} = (10 + 3 x) (10 - 3 x)$

Hence, $100 - 9 x^{2} = (10 + 3 x) (10 - 3 x)$

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