Question

Разложите на множители 5x^2-125 64-4y^2 ax^2-ay^2 x^3-xy^2 (x+y)^2-z^2 81-(a+2b)^2 (a+2b)^2-(a-2b)^2 (c+d)^2-(2c+3d)^2 a^2n-b^2m c^4n-d^4

Answer 1

5x²-125 = 5(x²-25)=5(x-5)(x+5)
64 - 4y² = 4(16 - y²) = 4(4-y)(4+y)
ax² - ay² = a(x² - y²) = a(x - y) (x+y)
x³-xy² = x(x² - y²) = x(x - y) (x+y)
(x+y)²-z² = (x+y-z)(x+y+z)
81 - (a+2b)² = (9 - a - 2b) (9 + a + 2b)
(a+2b)² -(a-2b)² =(a+2b-a+2b)(a+2b+a-2b)=4b*2a
(c+d)²-(2c+3d)²=(c+d+2c+3d)(c+d-3c-3d)=(3c+4d)(-2c-2d) =  = -2(c+d)(3c+4d)
a^2n - b^2m = (a^n - b^m)(a^n + b^m)
 c^4n -d^4 =(c^2n - d^2) (c^2n + d^2)