1.用因式分解进行简便运算 (1)(8又7/13)²-(8又1/12)²(2)(123又5/7)²-(76又2/7)²2.先把下列各式分解因式,再求值:(1)15x²(y+4)-30x(y+4),其中x=2,y=-2(2)5x(m-2)+4x
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![1.用因式分解进行简便运算 (1)(8又7/13)²-(8又1/12)²(2)(123又5/7)²-(76又2/7)²2.先把下列各式分解因式,再求值:(1)15x²(y+4)-30x(y+4),其中x=2,y=-2(2)5x(m-2)+4x](/uploads/image/z/248150-38-0.jpg?t=1.%E7%94%A8%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%E8%BF%9B%E8%A1%8C%E7%AE%80%E4%BE%BF%E8%BF%90%E7%AE%97+%EF%BC%881%EF%BC%89%EF%BC%888%E5%8F%887%2F13%EF%BC%89%26%23178%3B-%EF%BC%888%E5%8F%881%2F12%EF%BC%89%26%23178%3B%EF%BC%882%EF%BC%89%EF%BC%88123%E5%8F%885%2F7%29%26%23178%3B-%EF%BC%8876%E5%8F%882%2F7%EF%BC%89%26%23178%3B2.%E5%85%88%E6%8A%8A%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E5%88%86%E8%A7%A3%E5%9B%A0%E5%BC%8F%EF%BC%8C%E5%86%8D%E6%B1%82%E5%80%BC%EF%BC%9A%EF%BC%881%EF%BC%8915x%26%23178%3B%EF%BC%88y%2B4%29-30x%28y%2B4%29%EF%BC%8C%E5%85%B6%E4%B8%ADx%3D2%EF%BC%8Cy%3D-2%EF%BC%882%EF%BC%895x%EF%BC%88m-2%EF%BC%89%2B4x)
1.用因式分解进行简便运算 (1)(8又7/13)²-(8又1/12)²(2)(123又5/7)²-(76又2/7)²2.先把下列各式分解因式,再求值:(1)15x²(y+4)-30x(y+4),其中x=2,y=-2(2)5x(m-2)+4x
1.用因式分解进行简便运算 (1)(8又7/13)²-(8又1/12)²
(2)(123又5/7)²-(76又2/7)²
2.先把下列各式分解因式,再求值:
(1)15x²(y+4)-30x(y+4),其中x=2,y=-2
(2)5x(m-2)+4x(2-m),其中x=0.m=5.5
(3)(2x
+10²(3x-2)+x(2x+1)(2-3x),其中x=2/3
3.请用分解因式的方法计算一下各式:
(1)73²-27² (2)204²+204×192+96²
4.已知a²+b+2a-4b+5=0,求2a²+4b-3的值
5.已知xy=5,a-b=6,求½xya²-abxy+½xyb²的值
6.四个连续自然数的积加上1,是否能成为一个完全平方式?为什么?
7.已知实数a,b满足ab=1,a+b=3,求代数式a²b+ab²的值
1.用因式分解进行简便运算 (1)(8又7/13)²-(8又1/12)²(2)(123又5/7)²-(76又2/7)²2.先把下列各式分解因式,再求值:(1)15x²(y+4)-30x(y+4),其中x=2,y=-2(2)5x(m-2)+4x
考虑这几个公式
a^2 - b^2 = (a+b)*(a-b)
a^2+2ab+b^2 = (a+b)^2
a^2-2ab+b^2 = (a-b)^2
于是
1.(1) (16 + 7/13 + 1/12) * (7/13 - 1/12) = (16+ 97/156) * 71/156 = ...
(2) 200* (47+3/7) = ...
2.(1) 15x*(x-2)*(y+4) = 0
(2) x*(m-2) = 0.4*3.5 = 1.4
(3) 3x-2 = 0 因此就剩下 2x = 4/3
3 (1) 100*46 = 4600
(2) (204+96)^2 = 90000
4 (a+1)^2 + (b-2)^2 = 0 ==> a=-1,b=2
2a²+4b-3 = 2+8-3=7
5 1/2xy*(a-b)^2 = 5/2*6^2 = 90
6 (n-1)*n*(n+1)*(n+2)+1 = (n^2 -1)*[(n+1)^2 - 1] + 1
= [n(n+1)]^2 - n^2-(n+1)^2 + 2
=[n(n+1)]^2 - 2*n^2 - 2n + 1
=[n(n+1)-1]^2 是完全平方
7 a^2b+ab^2 = ab(a+b) = 1*3=3
都是平方差公式,a2-b2=(a+b)(a—b)