因式分解 4×175²-100×25 x²(x-y)+(y²-x²)

题目

因式分解 4×175²-100×25 x²(x-y)+(y²-x²)
x²(x-y)+(y²-x²)
4×175²-100×25

答案

x²(x-y)+(y²-x²)
=x²(x-y)-(x+y)(x-y)
=(x-y)(x²-x-y)
4×175²-100×25
=4×(175²-25²)
=4×(175+25)(175-25)
=4×200×150
=120000