Question

Factorise 256 a raise to 8 minus b raised to 8

Answer 1

$\mathfrak{Answer:-}$

$\tt{256a^{8} - b^{8}}$

=》$\tt{(2a)^{8} - (b)^{8}}$

=》$\tt{((2a)^{4})^{2} - ((b^{4})^{2})}$

=》$\tt{((2a)^{4} + b^{4}) ((2a)^{4} - b^{4})}$

=》$\tt{((2a)^{4} + b^{4}) (((2a)^{2})^{2} - ((b)^{2})^{2})}$

=》 $\tt{((2a)^{4} + b^{4}) ((2a)^{2} + b^{2}) ((2a)^{2} - b^{2})}$

=》 $\tt{((2a)^{4} + b^{4}) ((2a)^{2} + b^{2}) (2a + b)(2a - b)}$

Identity used :

$\sf{a^{2} - b^{2} = (a + b)(a - b)}$