a)
[tex]ab^2+a^2b=ab(a+b)=2\cdot5=10[/tex]
b)
[tex]a+b=5\ \ \ |()^2\\\\(a+b)^2=25\\\\a^2+2ab+b^2=25\\\\a^2+b^2=25-2ab\\\\a^2+b^2=25-2\cdot2\\\\a^2+b^2=25-4\\\\a^2+b^2=21[/tex]
c)
[tex]a^2b^4+a^4b^2=a^2b^2(b^2+a^2)=(ab)^2(a^2+b^2)=2^2\cdot21=4\cdot21=84[/tex]
d)
[tex]a^2+b^2=21\ \ \ |()^2\\\\(a^2+b^2)^2=441\\\\a^4+2a^2b^2+b^4=441\\\\a^4+b^4=441-2a^2b^2\\\\a^4+b^4=441-2(ab)^2\\\\a^4+b^4=441-2\cdot2^2\\\\a^4+b^4=441-2\cdot4\\\\a^4+b^4=441-8\\\\a^4+b^4=433[/tex]
