Factorise: |
(a) \[{{a}^{4}}-{{b}^{4}}\] |
(b) \[{{p}^{4}}-81\] |
(c) \[{{x}^{4}}-{{\left( y+z \right)}^{4~~}}\] |
(d) \[{{x}^{4}}-{{(x-z)}^{4}}\] |
Answer:
(a) \[{{a}^{4}}-{{b}^{4}}={{({{a}^{2}})}^{2}}-{{({{b}^{2}})}^{2}}\] \[=({{a}^{2}}-{{b}^{2}})({{a}^{2}}+{{b}^{2}})\] \[=(a-b)(a+b)({{a}^{2}}+{{b}^{2}})\] (b) \[{{p}^{4}}-81={{({{p}^{2}})}^{2}}-{{(9)}^{2}}\] \[=({{p}^{2}}-9)({{p}^{2}}+9)\] \[=[{{(p)}^{2}}-{{(3)}^{2}}]({{p}^{2}}+9)\] \[=(p-3)(p+3)({{p}^{2}}+9)\] (c) \[{{x}^{4}}-{{(y+z)}^{4}}={{({{x}^{2}})}^{2}}-{{\{{{(y+z)}^{2}}\}}^{2}}\] \[=\{{{x}^{2}}-{{(y+z)}^{2}}\}\{{{x}^{2}}+{{(y+z)}^{2}}\}\] \[=\{x-(y+z)\}\{x+(y+z)\}\{{{x}^{2}}+{{(y+z)}^{2}}\}\] \[=(x-y-z)(x+y+z)\{{{x}^{2}}+{{(y+z)}^{2}}\}\] (d) \[{{x}^{4}}-{{(x-z)}^{4}}={{({{x}^{2}})}^{2}}-{{\{{{(x-z)}^{2}}]}^{2}}\] \[=\{{{x}^{2}}-{{(x-z)}^{2}}\}\{{{x}^{2}}+{{(x-z)}^{2}}\}\] \[=(x-x+z)(x+x-z)\{{{x}^{2}}+{{(x-z)}^{2}}\}\]
You need to login to perform this action.
You will be redirected in
3 sec