Question

几道数学题帮帮忙

a的二次方(b-1)-(b-1) (因式分解) 需要过程
16(x+y)的二次方-25(x-y)的二次方(同上)
a的二次方(a-b)+b的二次方(b-a)(同上)

Answer 1

1.解：a²(b-1)-(b-1)=(b-1)(a²-1)=(b-1)(a+1)(a-1)
2.解：16(x+y)²-25(x-y)²=[4(x+y)]²-[5(x-y)]²=[4(x+y)+5(x-y)]×[4(x+y)-5(x-y)]=(9x-y)(9y-x)
3.解：a²(a-b)+b²(b-a)=a²(a-b)-b²(a-b)=(a-b)(a²-b²)=(a-b)²(a+b)

Answer 2

(1)
a²(b-1)-(b-1)
=(a²-1)(b-1)
=(a+1)(a-1)(b-1)

(2)
16(x+y)²-25(x-y)²
=[4(x+y)]²-[5(x-y)]²
=(4x+4y+5x-5y)(4x+4y-5x+5y)
=(9x-y)(9y-x)

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