[tex]1)\\ \sqrt[3]{\frac{1}{27}}\times9^{\frac{2}{3}} = \sqrt[3]{\frac{1}{27}}\times\sqrt[3]{9^{2}} = \sqrt[3]{\frac{1}{27}\times81} = \sqrt[3]{\frac{81}{27}} = \sqrt[3]{3}[/tex]
[tex]2)\\(3x+2)^{2}-(2x+1)(2x-1) = 9x^{2}+12x+4 - (4x^{2}-1) = 9x^{2}+12x+4-4x^{2}+1 = \\\\=5x^{2}+12x+5[/tex]
[tex]3)\\(x-11)^{2}+(2x-3)^{2} = x^{2}-22x+121 + 4x^{2}-12x+9 = 5x^{2}-34x +130[/tex]
[tex]4)\\3x-3 \leq 2x-3\\\\3x-2x \leq -3+3\\\\x \leq 0\\\\x \in (-\infty; 0 >[/tex]
[tex]5)\\8x+5 > 10x + 7\\\\8x - 10x > 7-5\\\\-2x> 2 \ \ /:(-2)\\\\x < -2\\\\x \in (-\infty;-1)[/tex]
Wykorzystano wzory skróconego mnożenia:
[tex](a+b)^{2} = a^{2}+2ab + b^{2}\\\\(a-b)^{2} = a^{2}-2ab + b^{2}\\\\(a+b)(a-b) = a^{2}-b^{2}[/tex]
