Question

因式分解求大神解答

Answer 1

2.
-x³+10x²y-25xy²
=-x(x²-10xy+25y²)
=-x(x-5y)²
4.
(x-y)^7 -4xy(y-x)^5
=(x-y)^7+4xy(x-y)^5
=(x-y)^5[(x-y)²+4xy]
=(x-y)^5 (x²-2xy+y²+4xy)
=(x-y)^5(x²+2xy+y²)
=(x-y)^5(x+y)²
6.
(a²+1/a²)²-4
=(a²+1/a²+2)(a²+1/a²-2)
=(a+1/a)²(a-1/a)²
8.
-2x^5+36x³-162x
=-2x(x⁴-18x²+81)
=-2x(x-9)²
10.
(a²-4b²)²+b(2a+5b)(2b-a)²
=[(a+2b)(a-2b)]²+(2ab+5b²)(a-2b)²
=(a+2b)²(a-2b)²+(2ab+5b²)(a-2b)²
=(a-2b)²[(a+2b)²+2ab+5b²]
=(a-2b)²(a²+4ab+4b²+2ab+5b²)
=(a-2b)²(a²+6ab+9b²)
=(a-2b)²(a+3b)²

2.
4x⁴+12x³+12x²+4x
=4x(x³+3x²+3x+1)
=4x(x+1)³
4.
x^6-3x⁴+3x²-1
=(x²-1)³
=[(x+1)(x-1)]³
=(x+1)³(x-1)³

2.
216x³+1
=(6x)³+1
=(6x+1)(36x²-6x+1)
4.
x^(3n)+y^(6n)
=(xⁿ)³+[y^(2n)]³
=[xⁿ+y^(2n)][x^(2n)-xⁿy^(2n)+y^(4n)]
6.
1-8(a+b)³
=1³-[2(a+b)]³
=[1-2(a+b)][1²+1×2(a+b)+4(a+b)²]
=(1-2a-2b)(1+2a+2b+4a²+8ab+4b²)