Question

求这两道题分解因式过程

1.-4(x+2y)²+9(2x-y)²
2.81x^4-1

Answer 1

1、-4(x+2y)^2+9(2x-y)^2
=(6x-3y)^2-(2x+4y)^2
=(6x-3y+2x+4y)(6x-3y-2x-4y)
=(8x-y)(4x-7y)
用到公式：a^2-b^2=(a+b)(a-b)
2、81x^4-1
=(9x^2+1)(9x^2-1)
=(9x^2+1)(3x+1)(3x-1)

Answer 2

平方差公式 a^2-b^2=(a+b)*(a-b)

1. -4(x+2y)²+9(2x-y)²=9(2x-y)²-4(x+2y)²=(3(2x-y)+2(4x+2y))*(3(2x-y)-2(x+2y))

2. 81x^4-1=(9x^2+1)*(9x^2-1)==(9x^2+1)*(3x+1)*(3x-1)

Answer 3

1前后换一下，完全平方式
a²-b²=(a+b)(a-b)