1/8-x^6
1/8=(1/2)^3
x^6=(x^2)^3
разность кубов a^3-b^3=(a-b)(a^2+ab+b^2)
воспользуемся этой формулой
(1/2-x^2)(x^4+1/4+x^2/2)
(2a – c)^2 = (2a)^2-2·2a·c +<span> c^</span>2 = 4a^<span>2 </span>– 4ac + c^2 квадрат разности
(2k<span> +</span><span> 3n</span>)^2<span> = (</span>2k)^2<span> + 2·</span>2k·3n<span> + (</span>3n)^2<span> = 4k^</span>2<span> + 12kn + 9n^</span>2 квадрат суммы
<span>9x^2</span><span> – </span><span>16y^2</span><span> = (</span>3x)^2<span> – </span>(4y)^2<span> = (</span>3x<span> – </span>4y)(3x<span> +</span><span> 4y</span>) разность квадратов
(3x<span> +</span><span> 2y</span>)^3<span> = (</span>3x)^3<span> + 3·</span><span>(3x)^2</span>·2y<span> + 3·</span>3x·<span>(2y)^2</span><span> + (</span>2y)^3<span> = 27x^</span>3<span> + 54x^</span>2y + 36xy^2<span> + 8y^</span>3 куб суммы
а) <span>64с^3</span><span> – </span>8<span> = (</span>4с)^3<span> – </span>2^3<span> = (</span>4с<span> – </span>2)((4с)^2<span> + </span>4с·2<span> + </span>2^2) = (4с – 2)(16с^2<span> + 8с + 4) разность кубов</span>