question_answer

Factorise the following:

(a) \[{{x}^{4}}-{{y}^{4}}\]

(b) \[16{{x}^{4}}-81\]

Answer:

(a) \[{{x}^{4}}{{y}^{4}}={{\left( {{x}^{2}} \right)}^{2}}{{\left( {{y}^{2}} \right)}^{2}}\]

\[=\left( {{x}^{2}}+\text{ }{{y}^{2}} \right)\left( {{x}^{2\text{ }}}{{y}^{2}} \right)\]

\[=\left( {{x}^{2}}+\text{ }{{y}^{2}} \right)\left( x+y \right)\left( xy \right)\]

(b) \[16{{x}^{4\text{ }}}81={{\left( 4{{x}^{2}} \right)}^{2}}{{\left( 9 \right)}^{2}}\]

\[=\left( 4{{x}^{2}}+9 \right)\left( 4{{x}^{2\text{ }}}9 \right)\]

\[=\left( 4{{x}^{2}}+9 \right)\left[ {{\left( 2x \right)}^{2}}{{\left( 3 \right)}^{2}} \right]\]

\[=\text{ }\left( 4{{x}^{2}}+9 \right)\left( 2x+3 \right)\left( 2x3 \right)\]