Type IV-Factorisation using identities — lesson. Mathematics CBSE, Class 8.

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Use the following identities to factorise the expressions.

$\begin{array}{l} {(a + b)}^{2} = a^{2} + 2 ab + b^{2} \\ {(a - b)}^{2} = a^{2} - 2 ab + b^{2} \\ a^{2} - b^{2} = (a + b) (a - b) \\ {(a + b)}^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3} \\ {(a - b)}^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3} \\ a^{3} + b^{3} = (a + b) (a^{2} - ab + b^{2}) \\ a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) \end{array}$

Example:

$y^3+64$

Let us write the above expression as

$y^3+4^3$ .

Use the identity,

$a^3+b^3 = (a+b)(a^2-ab+b^2)$ .