a).(2x-3)(2x-3) - (2x+3)(2x+3) x= -1/6 4x²-6x-6x+9 -(4x²+6x+6x+9) = 4x²-12x+9-4x²-6x-6x-9 = -24x -24 · (-1/6) = 4 b).(3a-2b)(3a+2b) - (2b-4a)(2b+4a) a= -1/5 b=3/7 9a²+6ab-6ab-4b² -(4b²+8ab-8ab-16a²) = 9a²-4b²-4b²-8ab+8ab+16a² =25a²-8b² 25 ·(-1/5)² - 8 ·(3/7)² = 25 ·1/25 - 8 · 9/49 = 1 - 72/49 = 49/49 - 72/49 = -23/49
[latex]a)\(2x-3)(2x-3)-(2x+3)(2x+3) = (2x-3)^{2}-(2x+3)^{2}=\\=4x^{2}-12x+9 - (4x^{2}+12x+9) = 4x^{2}-12x+9-4x^{2}-12x-9=-24x [/latex] [latex]dla x = -frac{1}{6}\\-24x = -24cdot(-frac{1}{6}) = frac{24}{6} = 4 [/latex] [latex]b)\(3a-2b)(3a+2b) - (2b-4a)(2b+4a) = 9a^{2}-4b^{2}-(4b^{2}-16a^{2})=\\=9a^{2}-4b^{2}-4b^{2}+16a^{2} = 25a^{2}-8b^{2}[/latex] [latex]dla a = -frac{1}{5}, b = frac{3}{7}\\25a^{2}-8b^{2} = 25cdot(-frac{1}{5})^{2}-8cdot(frac{3}{7})^{2}=25cdotfrac{1}{25}-8cdotfrac{9}{49}=1 - frac{72}{49} =\\=frac{49}{49}-frac{72}{49} = -frac{23}{49}[/latex] Wykorzystano wzory skróconego mnozenia: (a + b)² = a² + 2ab + b² (a - b)² = a² - 2ab + b² (a + b)(a - b) = a² - b²