\(a,\left(x^3+5x^2-2x+1\right)\left(x-7\right)\\ =x^4+5x^3-2x^2+x-7x^3-35x^2+14x-7\\ =x^4-2x^3-37x^2+15x-7\\ b,\left(2x^2-3xy+y^2\right)\left(x+y\right)\\ =2x^3-3x^2y+xy^2+2x^2y-3xy^2+y^3\\ =2x^3-x^2y-2xy^2+y^3\\ c,\left(x-2\right)\left(x^2-5x+1\right)-x\left(x^2+11\right)\\ =x^3-5x^2+x-2x^2+10x-2-x^3-11x\\ =-7x^2-2\\ d,x\left(1-3x\right)\left(4-3x\right)-\left(x-4\right)\left(3x+5\right)\\ =x\left(4-12x-3x+9x^2\right)-\left(3x^2-12x+5x-20\right)\\ =4x-12x^2-3x+9x^3-3x^2+12x-5x+20\\ =9x^3-15x^2+8x+20\)
`a// (x^3+5x^2-2x+1)(x-7)`
`=x^4-7x^3+5x^3-35x^2-2x^2+14x+x-7`
`=x^4-2x^3-37x^2+15x-7`
_________________________________________________________
`b// (2x^2-3xy+y^2)(x+y)`
`=2x^3+2x^2y-3x^2y-3xy^2+xy^2+y^3`
`=2x^3-x^2y-2xy^2+y^3`
_________________________________________________________
`c// (x-2)(x^2-5x+1)-x(x^2+11)`
`=x^3-5x^2+x-2x^2+10x-2-x^3-11x`
`=-7x^2-2`
_________________________________________________________
`d// x(1-3x)(4-3x)-(x-4)(3x+5)`
`=(x-3x^2)(4-3x)-(x-4)(3x+5)`
`=4x-3x^2-12x^2+9x^3-3x^2-5x+12x+20`
`=9x^3-18x^2+11x+20`
`a)`\(\left(x^3+5x^2-2x+1\right)\left(x-7\right)=x^4-7x^3+5x^3-35x^2-2x^2+14x+x-7=x^4-2x^3-37x^2+15x-7\)
`b)`\(\left(2x^2-3xy+y^2\right)\left(x+y\right)=2x^3+2x^2y-3x^2y-3xy^2+xy^2+y^3=2x^3-x^2y-2xy^2+y^3\)
`c)`\(\left(x-2\right)\left(x^2-5x+1\right)-x\left(x^2+11\right)=x^3-5x^2+x-2x^2+10x-2-x^3-11x=-7x^2-2\)
`d)`\(x\left(1-3x\right)\left(4-3x\right)-\left(x-4\right)\left(3x+5\right)=x\left(4-3x-12x+9x^2\right)-\left(3x^2+5x-12x-20\right)=4x-15x^2+9x^3-3x^2+7x+20=9x^3-18x^2+11x+20\)
