Выполните действия: (x-5)(5+x); (8+y)(y-8); (10-k)(k+10); (a+2/4b)(a-2/3b); (4/9x-y)(y+4/9x); (4/15n-m)(m+4/15n); (9x-5y)(9x+5y); (-4a+3b)(3b+4a); (13k-2d)(2d+13k); (5/4c+3/7d)(3/7d-5/4c); (1/3x-3y)(3y+1/3x); (1/5a+1/9b)(1/9b-1/5a).

Правило.

(a - b)(a + b) = a² - b²

Объяснение:

(x - 5)(5 + x) = (x - 5)(x + 5) = x² - 5² = x² - 25

(8 + y)(y - 8) = (y + 8)(y - 8) = y² - 8² = y² - 64

(10 - k)(k + 10) = (10 - k)(10 + k) = 10² - k² = 100 - k²

(a + 2/4 * b)(a - 2/3 * b) = a² + 2/4 * ba - 2/3 * ba - 2/6 * b² =

= a² + 6/12 * ba - 8/12 * ba - 2/6 * b² = a² - 2/12 * ba - 2/6 * b² =

= a² - 1/6 * ba - 2/6 * b²

или

(a + 2/3 * b)(a - 2/3 * b) = a² - (2/3 * b)² = a² - 4/9 * b²

или

(a + 2/4 * b)(a - 2/4 * b) = a² + (2/4 * b)² = a² + (1/2 * b)² =

= a² + 1/4 * b² = a² + 0,25b²

(4/9 * x - y)(y + 4/9 * x) = (4/9 * x - y)(4/9 * x + y) = (4/9 * x)² - y² =

= 16/81 * x² - y²

(4/15 * n - m)(m + 4/15 * n) =  (4/15 * n - m)(4/15 * n + m) =

= (4/15 * n)² - m² = 16/225 * n² - m²

(9x - 5y)(9x + 5y) = 81x² - 25y²

(-4a + 3b)(3b + 4a) = (3b - 4a)(3b + 4a) = 9b² - 16a²

(13k - 2d)(2d + 13k) = (13k - 2d)(13k + 2d) = 169k² - 4d²

(5/4 * c + 3/7 * d)(3/7 * d - 5/4 * c) =  (3/7 * d - 5/4 * c)(3/7 * d + 5/4 * c) =

= (3/7 * d)² - (5/4 * c)² = 9/49 * d² - 25/16 * c² = 9/49 * d² - 1,5625c²

(1/3 * x - 3y)(3y + 1/3 * x) = (1/3 * x - 3y)(1/3 * x + 3y) = (1/3 * x)² - 9y² =

= 1/9 * x² - 9y²

(1/5 * a + 1/9 * b)(1/9 * b - 1/5 * a) = (1/9 * b - 1/5 * a)(1/9 * b + 1/5 * a) =

= (1/9 * b)² - (1/5 * a)² = 1/81 * b² - 1/25 * a² = 1/81 * b² - 0,04a²