Question

因式分解2.（x+y）²+4(x-y)²-4(x²-y²)

3.a²+5ab+6b²+a+2b
4.x四次方-2x²+5x-4
5.-2负三次方-8负一次方×（-1）负二次方×（﹣½）负二次方×7º

Answer 1

1.原式=(x+y)² - 4(x+y)(x-y) + 4(x-y)²
=[(x+y) - 2(x-y)]²
=(3y-x)²

2.原式=a²+4ab+4b²+ab+2b²+a+2b
=(a+2b)² + b(a+2b) + (a+2b)
=(a+2b)[(a+2b)+b+1]
=(a+2b)(a+3b+1)

3.原式=x^4 - 1 - 2x² + 2 + 5x - 5
=(x^4 - 1) - 2(x² - 1) + 5(x-1)
=(x²+1)(x²-1) - 2(x+1)(x-1) + 5(x-1)
=(x²+1)(x+1)(x-1) - 2(x+1)(x-1) + 5(x-1)
=(x-1)[(x²+1)(x+1) - 2(x+1) + 5]
=(x-1)(x³+x²-x+4)

4.原式=1/(-2)³ - (1/8)×[1/(-1)²]×[1/(-1/2)²]×1
=(-1/8) - (1/8)×1×4×1
=(-1/8)(1+4)
=-5/8

追问

第四个是为什么这么算啊

Answer 2

2.（x+y）²+4(x-y)²-4(x²-y²) =x^2+2xy+y^2+4X^2-8XY+4Y^2-4X^2+4Y^2=x^2-6xy+9y^2=(x-3y)^2
3.a²+5ab+6b²+a+2b=(x+2b)(a+3b)+(a+2b)=(a+2b)(a+3b+1)
4.x四次方-2x²+5x-4=(x^2-1)^2+5(x-1)=(x+1)^2(x-1)^2+5(x-1)=(x-1)[(x+1)^2(x-1)+5]
5.-2负三次方-8负一次方×（-1）负二次方×（﹣½）负二次方×7º
=-1/8-1/8*1*4*1=-1/2