[tex](a+b)(c+d) = a\cdot c+a\cdot d+b\cdot c+b\cdot d[/tex]
[tex]a) \ (4a+3)(b+5) = 4a\cdot b + 4a\cdot5 + 3\cdot b+3\cdot5 = 4ab+20a + 3b + 15\\\\\\b) \ (5a-b)(a-3) = 5a\cdot a +5a\cdot(-3) -b\cdot a -b\cdot (-3) = 5a^{2}-15a-ab+3b\\\\\\c) \ (3x-y)(2x+y) = 3x\cdot2x +3x\cdot y -y\cdot2x-y\cdot y = 6x^{2}+3xy -2xy-y^{2}=6x^{2}+xy-y^{2}[/tex]
[tex]d) \ (2xy+3x)(xy-2x) = 2xy\cdot xy +2xy \cdot(-2x) + 3x\cdot xy + 3x\cdot(-2x) =\\\\= 2x^{2}y^{2}-4x^{2}y +3x^{2}y -6x^{2}= 2x^{2}y^{2}-x^{2}y - 6x^{2}[/tex]
