Question

factorise the following expressions 1)b^4-100 2)144-a^6 3)b^4-a^2

Answer 1

$\\ 1) b^{4} - 10^{2} \\ \\ (b^{2})^{2} - 10^{2} \\ (b^{2}-10)(b^{2}+10)\\ \boxed{(b - \sqrt10)(b + \sqrt10)(b^{2}+10)}$

$\\ 2) (b^{2})^{2} - a^{2} \\ \\(b^{2} - a)(b^{2} + a) \\ \boxed{( b - \sqrt a)(b+\sqrt a)(b^{2} + a)}$

$\\ 3) 12^{2} - (a^{3})^{2}\\ \boxed{(12-a^{3})(12+a^{3})}$

Answer 2

Hello!

$\bf{1.)} \: \sf b^{4} - 100 \\ \implies \sf (b^{2})^{2} - (10)^{2} \\ \implies \sf (b^{2} - 10)(b^{2} + 10) \\ \implies \boxed{\red{\bf{(b- \sqrt{10})(b + \sqrt{10})(b^{2} + 10)}}}$

$\bf{2.)} \: \sf 144- a^{6} \\ \implies \sf (12)^{2} - \sf (a^{3})^{2} \\ \implies \boxed{\red{\bf{(12+a^{3})(12-a^{3})}}}$

$\bf{3.)} \: \sf b^{4} - a^{2} \\ \implies \sf (b^{2} + a)(b^{2} - a) \\ \implies \boxed{\red{\bf{(b- \sqrt{a})(b + \sqrt{a})(b^{2} + a)}}}$

Cheers!