Answer:
[tex]\mathrm{1.\:3n^2\left(-4nm^2+9+7n\right)}[/tex]
[tex]\mathrm{2.\:4x^2y^4\left(x^2y^3-x+1\right)}[/tex]
[tex]\mathrm{3.\:6\left(2y-7x-3\right)}[/tex]
[tex]\mathrm{4.\:3x^3\left(9x+2xy-10\right)}[/tex]
[tex]\mathrm{5.\:2v^4\left(4v^2u+7v+8\right)}[/tex]
Step-by-step explanation:
[tex]\mathrm{1.\: -12n^3m^2 + 27n^2 + 21n^3}\\\\\mathrm{=-12n^2n+27n^2+21n^2n}\\\\\mathrm{=4\cdot \:3n^2n+9\cdot \:3n^2+7\cdot \:3n^2n}\\\\\mathrm{=3n^2\left(-4nm^2+9+7n\right)}[/tex]
[tex]\mathrm{2.\: 4x^4y^7-4x^3y^4+4x^2y^4}\\\\\mathrm{=4x^2x^2y^4y^3-4x^2xy^4+4x^2y^4}\\\\\mathrm{=4x^2y^4\left(x^2y^3-x+1\right)}[/tex]
[tex]\mathrm{3.\: 12y-42x-18}\\\\\mathrm{=2\cdot \:6y+7\cdot \:6x+3\cdot \:6}\\\\\mathrm{=6\left(2y-7x-3\right)}[/tex]
[tex]\mathrm{4.\: 27x^4 + 6x^4y - 30x^3}\\\\\mathrm{=27x^3x+6x^3xy-30x^3}\\\\\mathrm{=9\cdot \:3x^3x+2\cdot \:3x^3xy+10\cdot \:3x^3}\\\\\mathrm{=3x^3\left(9x+2xy-10\right)}[/tex]
[tex]\mathrm{5.\:8v^6u+14v^5+16v^4}\\\\\mathrm{=8v^4v^2+14v^4v+16v^4}\\\\\mathrm{=4\cdot \:2v^4v^2+7\cdot \:2v^4v+4\cdot \:2\cdot \:2v^4}\\\\\mathrm{=2v^4\left(4v^2u+7v+8\right)}[/tex]
