Ответ:

Объяснение:

a)[tex]x^{5} +4ax^{3}- 4ax^{4}=x^{3}(x^{2}+4a-4ax^{2})[/tex]

б)4[tex]a^{6} -12a^{5}b+9a^{4}b^{2} =a^{4}(4a^{2}-12ab+9b^{2}) =a^{4}(2a-3b)^2[/tex]

в)[tex]\frac{1}{4}y^{4} +\frac{1}{9}y^{2}c^{2} -\frac{1}{3}y^{3}c=y^{2}(\frac{1}{4} y^{2} +\frac{1}{9}c^{2}-\frac{1}{3}yc)[/tex]

г)[tex]\frac{4}{9}b^{5}+4b^{3}c+9bc^{2}=b(\frac{4}{9}b^{4}+4b^2c+9c^{2})[/tex]

д)[tex]\frac{1}{4}x^{2} -y^{2} +(\frac{1}{2} }x+y)^2 =(\frac{1}{2}x-y)(\frac{1}{2}x+y)+(\frac{1}{2}x+y)^2=(\frac{1}{2}x+y)(\frac{1}{2}x-y+\frac{1}{2}x+y)=(\frac{1}{2}x+y)x[/tex]

е)[tex]\frac{1}{4}x^{2} -y^{2}-(\frac{1}{2}x-y)^2=\frac{1}{4}x^{2}-y^{2}-\frac{1}{4}x^{2}+xy-y^{2}=xy-2y^{2}=y(x-2y)[/tex]