Question

因式分解(13)16(x+y)²-25(x-y)² (14)a²(a-b)+b²(b-a)

Answer 1

(13)16(x+y)²-25(x-y)² \
=(4x+4y+5x-5y)(4x+4y-5x+5y)
=(9x-y)(-x+9y)

(14)a²(a-b)+b²(b-a)
=(a-b)(b²-a²)
=(a-b)(a+b)(b-a)
=-(a-b)²(a+b）

Answer 2

(13) 16(x+y)^2-25(x-y)^2=-(9x^2-82xy+9y^2)=-(x-9y)(9x-y)
(14)a^2(a-b)+b^2(b-a)=a^3-ab^2+b^3-ba^2=a(a^2-b^2)+b(b^2-a^2)=(a-b)(a^2-b^2)=(a-b)^2(a+b)