将下列各式因式分解:①x²+7x+10 ②x²-3xy-10y²③16x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
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![将下列各式因式分解:①x²+7x+10 ②x²-3xy-10y²③16x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](/uploads/image/z/1008809-17-9.jpg?t=%E5%B0%86%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%EF%BC%9A%E2%91%A0x%26%23178%3B%2B7x%2B10+%E2%91%A1x%26%23178%3B-3xy-10y%26%23178%3B%E2%91%A216x%E5%9B%9B%E6%AC%A1%E6%96%B9-y%E5%9B%9B%E6%AC%A1%E6%96%B9+%E2%91%A3%EF%BC%88x%26%23178%3B%2B4%EF%BC%89%26%23178%3B-16x%26%23178%3B+%E2%91%A4-3a%26%23179%3Bb-6a%26%23178%3Bb%26%23178%3B-3ab%26%23179%3B+%E2%91%A5a%26%23178%3B-b%26%23178%3B-c%26%23178%3B-2bc+%E2%91%A6%EF%BC%88m%26%23178%3B-1%EF%BC%89%26%23178%3B-6%EF%BC%88m%26%23178%3B-1%EF%BC%89%2B9)
将下列各式因式分解:①x²+7x+10 ②x²-3xy-10y²③16x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
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
将下列各式因式分解:①x²+7x+10 ②x²-3xy-10y²③16x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
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
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+...
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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
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