question_answer

Factorise the following:

(a) \[4{{x}^{2}}-20x+25\]

(b) \[{{x}^{4}}-256\]

Answer:

(a) \[4{{x}^{2}}-20x+25={{(2x)}^{2}}-2\times 2x\times 5+{{(5)}^{2}}\]

\[={{\left( 2x-5 \right)}^{2~}}~\] \[[\,Since,{{a}^{2}}-2ab+{{b}^{2}}={{(a-b)}^{2}}]\]

\[=\left( 2x-5 \right)\left( 2x-5 \right)~\]

(b) \[{{x}^{4}}-256={{({{x}^{2}})}^{2}}-{{(16)}^{2}}\]

\[=({{x}^{2}}+16)({{x}^{2}}-16)\]

\[\left[ using\text{ }{{\text{a}}^{2}}-{{b}^{2}}=\left( a+b \right)\left( a-b \right) \right]\]

\[=({{x}^{2}}+16)({{x}^{2}}-{{4}^{2}})\]

\[=({{x}^{2}}+16)(x+4)(x-4)\]