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

а) 16x⁴-81y⁴=(4x²-9y²)(4x²+9y²)=(2x-3y)(2x+3y)(4x²+9y²) б) 48a⁴-3b⁴=3(16a⁴-b⁴)=3(4a²-b²)(4a²+b²)=3(2a-b)(2a+b)(4a²+b²) в) 1/81*m⁸-1=(1/9*m⁴-1)(1/9*m⁴+1)=(1/3*m²-1)(1/3*m²+1)(1/9*m⁴+1) г) 32-1/2*m⁶=16-m⁶=(4-m³)(4-m³)

[latex]a^2-b^2=(a-b)(a+b) \\\ a^3\pm b^3=(a\pm b)(a^2\mp ab+b^2)[/latex] [latex]16x^4-81y^4=(4x^2-9y^2)(4x^2+9y^2)=(2x-3y)(2x-3y)(4x^2+9y^2)[/latex] [latex] 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)[/latex] [latex] \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)[/latex] [latex]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)[/latex]