Question

将下列各式因式分解：①x²+7x+10 ②x²-3xy-10y²

③16x四次方-y四次方 ④（x²+4）²-16x² ⑤-3a³b-6a²b²-3ab³ ⑥a²-b²-c²-2bc ⑦（m²-1）²-6（m²-1）+9 ⑧（a²+b²）²-4a²b²

Answer 1

①x²+7x+10 =(x+5)(x+2)
②x²-3xy-10y²=(x-5y)(x+2y)
③16x四次方-y四次方=(4x²+y²)(4x²-y²)=(4x²+y²)(2x+y)(2x-y)
④（x²+4）²-16x²=(x²+4+4x)(x²+4-4x)=(x+2)²(x-2)²
⑤-3a³b-6a²b²-3ab³ =-3ab(a²+2ab+b²)=-3ab(a+b)²
⑥a²-b²-c²-2bc =a²-(b²+2bc+c²)=a²-(b+c)²=(a+b+c)(a-b-c)
⑦（m²-1）²-6（m²-1）+9 =[(m²-1)-3]²=(m²-4)²=(m+2)²(m-2)²
⑧（a²+b²）²-4a²b²=(a²+b²+2ab)(a²+b²-2ab)=(a+b)²(a-b)²

Answer 2

①x²+7x+10 =(x+2)(x+5)
②x²-3xy-10y²=(x-5y)(x+2y)
③16x四次方-y四次方 =（4x²+y²)(4x²-y²)=(4x²+y²)(2x+y)(2x-y)
④（x²+4）²-16x² =(x²+4+4x)(x²+4-4x)=(x+2)²(x-2)²
⑤-3a³b-6a²b²-3ab³ =-3ab(a²+2ab+b²)=-3ab(a+b)²
⑥a²-b²-c²-2bc =a²-(b²+2bc+c²)=a²-(b+c)²=(a+b+c)(a-b-c)
⑦（m²-1）²-6（m²-1）+9 =(m²-1-3)²=(m+2)²(m-2)²
⑧（a²+b²）²-4a²b²=(a²+b²+2ab)(a²+b²-2ab)=(a+b)²(a-b)²

Answer 3

1.
x²+7x+10=(x+2)(x+5)
2.
x²-3xy-10y²=(x-5y)(x+2y)
3.
16x⁴-y⁴=(4x²+y²)(4x²-y²)=(4x²+y²)(2x+y)(2x-y)
4.
(x²+4)²-16x²
=[(x²+4)+4x][(x²+4)-4x]
=(x²+4x+4)(x²-4x+4)
=(x+2)²(x-2)²
5.
-3a³b-6a²b²-3ab³
=-3ab(a²+2ab+b²)
=-3ab(a+b)²
6.
a²-b²-c²-2bc
=a²-(b²+2bc+c²)
=a²-(b+c)²
=[a+(b+c)][a-(b+c)]
=(a+b+c)(a-b-c)
7.
(m²-1)²-6(m²-1)+9
=[(m²-1)-3]²
=(m²-4)²
=[(m+2)(m-2)]²
=(m+2)²(m-2)²
8.
(a²+b²)²-4a²b²
=(a²+b²+2ab)(a²+b²-2ab)
=(a+b)²(a-b)²