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CatLove2014 @CatLove2014

July 2021 1 11 Report

Разложите на множители:
а) [tex] 16x^{4} - 81y^{4} [/tex]
б) [tex] 48a^{4} - 3b^{4} [/tex]
в) [tex] \frac{1}{81}m^{8} - 1[/tex]
г) 32 - [tex] \frac{1}{2}m^{6} [/tex]

Answers & Comments

Artem112

Verified answer

$a^2-b^2=(a-b)(a+b)
\\\
a^3\pm b^3=(a\pm b)(a^2\mp ab+b^2)$

$16x^4-81y^4=(4x^2-9y^2)(4x^2+9y^2)=(2x-3y)(2x-3y)(4x^2+9y^2)$

$48a^{4} - 3b^{4} =3( 16a^{4} - b^{4} )=3(4a^2-b^2)(4a^2+b^2)=
\\\
=3(2a-b)(2a+b)(4a^2+b^2)$

$\frac{1}{81}m^{8} - 1=( \frac{m^4}{9} -1)( \frac{m^4}{9} +1)=( \frac{m^2}{3} -1)( \frac{m^2}{3} +1)( \frac{m^4}{9} +1)=
\\\
=( \frac{m}{ \sqrt{3} } -1)( \frac{m}{ \sqrt{3} } +1)( \frac{m^2}{3} +1)( \frac{m^4}{9} +1)$

$32 - \frac{1}{2}m^{6} = \frac{1}{2}(64-m^6)= \frac{1}{2}(8-m^3)(8+m^3)=
\\\
= \frac{1}{2}(2-m)(4+2m+m^2)(2+m)(4-2m+m^2)$

4 votes Thanks 4

CatLove2014 Спасибо :)

Answers & Comments

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