Question

1)fatore de forma completa os polinômios :
ajudem pf estou precisando das respostas .

Answer 1

$a) \ a^4-b^4=(a^2+b^2)(a^2-b^2)=(a^2+b^2)(a+b)(a-b)\\ b) \ 3x^2-6x+3=3(x^2-2x+1)=3(x-1)^2\\ c) \ 5a^2+30ab+45b^2=5(a^2+6ab+9b^2)=5(a+3)^2\\ d) \ m^2x-x=x(m^2-1)=x(m+1)(m-1)\\ e) \ x^3y-xy^3=xy(x^2-y^2)=xy(x+y)(x-y)\\ f) \ m^8-n^8=(m^4+n^4)(m^4-n^4)=(m^4+n^4)(m^2+n^2)(m^2-n^2)=\\ (m^4+n^4)(m^2+n^2)(m+n)(m-n\\ g) \ x^3-xy^2+x^2y-y^3=x(x^2-y^2)+y(x^2-y^2)=\\ (x^2-y^2)(x+y)=(x+y)(x-y)(x+y)$
$h) \ a^4-ax^3=a(a^3-x^3)=a(a-x) (a^2+a x+x^2)\\ i) \ 1-\frac{16}{x^4}=1-(\frac{1}{2})^4=(1+(\frac{1}{2})^2)(1-(\frac{1}{2})^2)=\\ (1+(\frac{1}{2})^2)(1+\frac{1}{2})(1-\frac{1}{2})\\ \\ j) \ y^3+\frac{4}{3}y^2+\frac{4}{9}y=y(y^2+\frac{4}{3}y+\frac{4}{9})=y(y+\frac{2}{3})^2$