a)
[tex](4a+1)(2a-5)=4a\cdot2a-4a\cdot5+1\cdot2a-1\cdot5=\\\\=8a^2-20a+2a-5=\boxed{8a^2-18a-5}[/tex]
b)
[tex](2x+3y)(5x+2y)=2x\cdot5x+2x\cdot2y+3y\cdot5x+3y\cdot2y=\\\\=10x^2+4xy+15xy+6y^2=\boxed{10x^2+19xy+6y^2}[/tex]
c)
[tex](3a+2b)(a-4b)=3a\cdot a-3a\cdot4b+2b\cdot a-2b\cdot4b=\\\\=3a^2-12ab+2ab-8b^2=\boxed{3a^2-10ab-8b^2}[/tex]
d)
[tex](2x-3y)(3x-2y)=2x\cdot3x-2x\cdot2y-3y\cdot3x-3y\cdot(-2y)=\\\\=6x^2-4xy-9xy+6y^2=\boxed{6x^2-13xy+6y^2}[/tex]
e)
[tex](a+2b)(5a-2b)=a\cdot5a-a\cdot2b+2b\cdot5a-2b\cdot2b=\\\\=5a^2-2ab+10ab-4b^2=\boxed{5a^2+8ab-4b^2}[/tex]
f)
[tex](5a^2-b)(2b-3a)=5a^2\cdot2b-5a^2\cdot3a-b\cdot2b-b\cdot(-3a)=\\\\=\boxed{10a^2b-15a^3-2b+3ab}[/tex]
