[tex]zad.3\\\\a)~~(2x+6)\cdot (3y+2x)=2x\cdot 3y + 2x\cdot 2x +6\cdot 3y+6\cdot 2 x = 6xy+4x^{2} +18y+12x\\\\b)~~(2x+6)\cdot (2x-6)=2x\cdot 2x -2x\cdot 6 +6\cdot2x - 6\cdot 6 =4x^{2} -12x+12x-36=4x^{2} -36\\lub\\korzystam~~ze~~wzoru~~skoconego~~mnozenia:~~(x-y)\cdot (x+y)=x^{2} -y^{2} \\\\(2x+6)\cdot (2x-6)=(2x)^{2} -6^{2} =4x^{2} -36\\\\c)~~x\cdot (x+2)\cdot (x-2)=(x^{2} +2x)\cdot (x-2)=x^{2} \cdot x -x^{2} \cdot 2 +2x\cdot x - 2x\cdot 2 =x^{3} -2x^{2} +2x^{2} -4x=x^{3}-4x\\lub\\[/tex]
[tex]korzystam~~ze~~wzoru~~skoconego~~mnozenia:~~(x-y)\cdot (x+y)=x^{2} -y^{2}\\\\x\cdot (x+2)\cdot (x-2)=x\cdot (x^{2} -4)=x\cdot x^{2} -x\cdot 4 =x^{3} -4x[/tex]
[tex]d)~~(2a+b)\cdot (3c+d)=2a\cdot 3c +2a\cdot d +b\cdot 3c + b\cdot d =6ac+2ad +3bc + bd[/tex]
