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) \[{{x}^{4}}-256={{({{x}^{2}})}^{2}}-{{(16)}^{2}}\] \[=({{x}^{2}}+16)({{x}^{2}}-16)\] \[\left[ using\text{ }{{\text{a}}^{2}}-{{b}^{2}}=\left( a+b \right)\left( a-b \right) \right]\] \[=({{x}^{2}}+16)({{x}^{2}}-{{4}^{2}})\] \[=({{x}^{2}}+16)(x+4)(x-4)\]
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