Odpowiedź:
[tex]a) \ (x+5)^{2} = x^{2}+2\cdot x \cdot 5 + 5^{2} = x^{2}+10x+25\\\\b) \ (x-4)^{2} = x^{2}-2\cdot x\cdot4 + 4^{2} = x^{2}-8x+16\\\\c) \ (x-3)(x+3) = x^{2}-3^{2} = x^{2}-9\\\\d) \ (2y\cdot6x)^{2} = (2y)^{2}\cdot(6x)^{2} = 4y^{2}\cdot36x^{2} = 144x^{2}y^{2}\\\\e) \ (8x-y^{3})^{2} = (8x)^{2}-2\cdot8x\cdot y^{3}+(y^{3})^{2} = 64x^{2}-16xy^{3}+y^{6}\\\\f) \ (6a-2b)(6a+2b) = (6a)^{2}-(2b)^{2} = 36a^{2}-4b^{2}[/tex]
Szczegółowe wyjaśnienie:
Korzystamy ze wzorów 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]