[tex]\bold{Hello!}\\\bold{Your~Answer~Is~Below!}[/tex]
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[tex]\bold{Solution~Steps:}[/tex]
[tex]1.)~Rewrite: 64x^6-1~as~(8x^3)^2-1^2[/tex]
- [tex]The~difference~of~squares~can~be~factored~using~the~rule:[/tex]
[tex]a^2-b^2=(a-b)(a+b)[/tex]
[tex]\bold{(8x^3-1)(8x^3+1)}[/tex]
[tex]2.)~Rewrite:~8x^3-1~as~(2x)^3-1^3[/tex]
- [tex]The~difference~of~cubes~can~be~factored~using~the~rule:[/tex]
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
[tex]\bold{(2x+1)(4x^2+2x+1}[/tex]
[tex]3.)~Rewrite:~8x^3+1~as~(2x)^3+1^3[/tex]
- [tex]The~sum~of~cubes~can~be~factored~using~the~rule:[/tex]
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
[tex]\bold{(2x+1)(4x^2-2x+1)}[/tex]
[tex]4.)~Rewrite~the~complete~factored~expression:[/tex]
- [tex]The~following~polynomials~are~not~factored~since~they~do~not~have~any~rational~roots:[/tex]
[tex](4x^2-2x+1),~(4x^2+2x+1)[/tex]
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[tex]\bold{Answers:}[/tex]
- [tex]Factored~Form:~\bold{(2x-1)(4x^2-2x+1)(2x+1)(4x^2+2x+1)}[/tex]
- [tex]Evaluated~Form:~\bold{(4x^2-1)((4x^2+1)^2-4x^2)}[/tex]
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[tex]\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~-TotallyNotTrillex}[/tex]
