Question

Valendo 100 pts :dados os polinomios A= 3x-4+y, B= x+15y e C= 5+ $yx^{2}$ caucule a expressao :
2A + BC
BA
3AB -C
d- A - BC

Answer 1

$A=3x-4+y\\\\B=x+15y\\\\C=5+yx^2$



$2A + BC\\\\2(3x-4+y)+(x+15y)(5+yx^2)\to\\\\ 6x-8+2y+5x+yx^3+75y+15y^2x^2\to\\\\ yx^3+15y^2x^2+75y+2y+6x+5x-8\to\\\\ \large\boxed{ yx^3+15y^2x^2++77y+11x-8 }$





$BA\\\\(x+15y)(3x-4+y)\to\\\\ 3 x^{2} -4x+xy+45xy-60y+15y^2\to\\\\ 3 x^{2} +15y^2+xy+45xy-4x-60y \\\\ \large\boxed{ 3 x^{2} +15y^2+46xy-4x-60y }$





$3AB -C\\\\ 3(3x-4+y)(x+15y)-5+yx^2\to\\\\ 3(3 x^{2}+45xy -4x-60y+xy+15y^2) -5+yx^2\to\\\\ 3( 3 x^{2} +15y^2+46xy-4x-60y )-5+yx^2\to\\\\9x^2+45y^2+138xy-12x-180y-5+xy^2\to\\\\ \large\boxed{ xy^2+9x^2+45y^2+138xy-12x-180y-5 }$





$A - BC\\\\ 3x-4+y-(x+15y)(5+yx^2)\to\\\\ 3x-4+y-(5x+yx^3+75y+15y^2x^2)\to\\\\ 3x-4+y-5x-yx^3-75y-15y^2x^2\to\\\\ -yx^3-15y^2x^2+3x-5x+y-75y-4\to\\\\ \large\boxed{ -yx^3-15y^2x^2-2x-74y-4 }$