Question

因式分解 x(x-y)-y(y-x) m²(x-1)+4(1-x) a²-4(a-b)²

Answer 1

x(x-y)-y(y-x)= x(x-y)+y(x-y)=(x+y)(x-y)

m²(x-1)+4(1-x) =m²(x-1)-4(x-1)=(m²-4)(x-1)=(m+2)(m-2)(x-1)

a²-4(a-b)² =(a+2a-2b)(a-2a+2b)=(3a-2b)(-a+2b)

(2x-3y)²-4x² (3x+y)² =(2x-3y)²-(6x²+2xy)²=(2x-3y+6x²+2xy)(2x-3y-6x²-2xy)

9(a-b)²-16(a+b)²=(3a-3b)²-(4a+4b)²=(3a-3b+4a+4b)(3a-3b-4a-4b)=(7a+b)(-a-7b)

49(m-n)²-9(m+n)²=(7m-7n)²-(3m+3n)²=(7m-7n+3m+3n)(7m-7n-3m-3n)=(10m-4n)(4m-10n)

=4(5m-2n)(2m-5n)