八年级上册数学因式分解
答案:2 悬赏:60
解决时间 2021-03-03 09:00
- 提问者网友：南佳人～
- 2021-03-03 05:58
最佳答案
- 二级知识专家网友：嗷呜我不好爱
- 2021-03-03 07:37
解(1) 16a^4-b^4 ^表示乘方
=(4a²)²-(b²)²
=(4a²+b²)(4a²-b²)
=(4a²+b²)(2a+b)(2a-b)
解(2) a²(m-n)+b²(n-m)
=a²(m-n)-b²(m-n)
=(m-n)(a²-b²)
=(m-n)(a+b)(a-b)
解(3) 3(a+1)²-75(a-4)²
=3[(a+1)²-25(a-4)²]
=3﹛(a+1)²-[5(a-4)]²﹜
=3[(a+1)+5(a-4)][(a+1)-5(a-4)]
=3(a+1+5a-20)(a+1-5a+20)
=3(6a-19)(-4a+21)
=-3(6a-19)(4a-21)
解(4) a^(2n+1)-16a^(2n-1)
=[a^(2n-1)]×(a²-16)
=[a^(2n-1)](a+4)(a-4)
解(5) 9(a-b)²-25(a+b)²
=[3(a-b)]²-[5(a+b)]²
=[3(a-b)+5(a+b)][(3(a-b)-5(a+b)]
=(3a-3b+5a+5b)(3a-3b-5a-5b)
=(8a+2b)(-2a-8b)
= -4(4a+b)(a+4b)
=(4a²)²-(b²)²
=(4a²+b²)(4a²-b²)
=(4a²+b²)(2a+b)(2a-b)
解(2) a²(m-n)+b²(n-m)
=a²(m-n)-b²(m-n)
=(m-n)(a²-b²)
=(m-n)(a+b)(a-b)
解(3) 3(a+1)²-75(a-4)²
=3[(a+1)²-25(a-4)²]
=3﹛(a+1)²-[5(a-4)]²﹜
=3[(a+1)+5(a-4)][(a+1)-5(a-4)]
=3(a+1+5a-20)(a+1-5a+20)
=3(6a-19)(-4a+21)
=-3(6a-19)(4a-21)
解(4) a^(2n+1)-16a^(2n-1)
=[a^(2n-1)]×(a²-16)
=[a^(2n-1)](a+4)(a-4)
解(5) 9(a-b)²-25(a+b)²
=[3(a-b)]²-[5(a+b)]²
=[3(a-b)+5(a+b)][(3(a-b)-5(a+b)]
=(3a-3b+5a+5b)(3a-3b-5a-5b)
=(8a+2b)(-2a-8b)
= -4(4a+b)(a+4b)
全部回答
- 1楼网友：时光挺欠揍
- 2021-03-03 08:23
1，(x+y)²-9y² =）(x+y-3y))x+y+3y)=(x-27)(x+47);
2,a²-b²+a+b = ( a+b)(a-b)+(a+b)=(a+b)(a-b+1);
3,10b(x-y)²-5a(y-x)²=10b(x-y)²-5a(x-y)²=5(x-y)²(2b-a);
4,(ab+b)²-(a+1)² =b ²(a+1)²-(a+1)²=(b ² -1) (a+1)²=(b-1)(b+1)(a+1)²;
5,(a²-x²)²-4ax(x-a)² ={(a+x)(a-x)}²-4ax(a-x)² = (a-x)² {a²+2ax+x²-4ax}= (a-x)² (a-x)² =(a-x)^4
6、（x+y+z)²-(x-y+z)²=（x+z)²+2(x+z)y+y² -(x+z)²+2(x+z)y-y²=4(x+z)
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