[tex]zad.3\\\\a)~~x^{2} +10x+25=x^{2} +2\cdot 5\cdot x+5^{2} = (x+5)^{2} \\\\b)~~9x^{2} +6x+1= (3x)^{2} +2\cdot 3x\cdot 1+1^{2}= (3x+1)^{2} \\\\c)~~a^{2} -12a+36= a^{2} -2\cdot 6\cdot a+6^{2} = (a-6)^{2} \\\\d)~~25y^{2} -30y +9=(5y)^{2} -2\cdot 5y\cdot 3 +3^{2} =(5y-3)^{2} \\\\e)~~4x^{2} +20x+25=(2x)^{2} +2\cdot 2x\cdot 5+5^{2} =(2x+5)^{2} \\\\f)~~100b^{2} -60b+9=(10b)^{2} -2\cdot 10b\cdot 3+3^{2} =(10b-3)^{2} \\[/tex]
[tex]zad.4\\\\a)~~4x^{2} -25=(2x)^{2} -5^{2} =(2x-5)\cdot (2x+5)\\\\b)~~9a^{2} -16b^{2} =(3a)^{2} -(4b)^{2} =(3a-4b)\cdot (3a+4b)\\\\c)~~\dfrac{4}{25} x^{2} -1=(\dfrac{2}{5} x)^{2} -1^{2} =(\dfrac{2}{5} x -1)\cdot (\dfrac{2}{5} x +1)\\\\d)~~0,81a^{2} -36b^{2} =(0,9a)^{2} -(6b)^{2} =(0,9a-6b)\cdot (0,9a+6b)\\[/tex]
korzystam ze wzorów skróconego mnożenia:
[tex]x^{2} -y^{2} =(x-y)\cdot (x+y)\\\\x^{2} -2\cdot x\cdot y +y^{2} =(x-y)^{2} \\\\x^{2} +2\cdot x\cdot y +y^{2} =(x+y)^{2}[/tex]
