Question

因式分解、平方差公式进行分解

初二上星期数学。

1.x²(y-4)-(y-4)

2.2x²-32

3.已知a+b=8且a²-b²=48.则a-3b=

4.x²-4y²

5.-x²+x²y²

6.a²(a-b)+b²(b-a)

7.(a+b)²-(a-b)²

8.4x²-5

9.x²-16

10.x^3+x²y-xy²-y^3

11.(5m²+3n²）²-（3m²+5n²）²

一题10分。 麻烦大家勒。

能答几题答几题、 别用错公式勒。是平方差公式进行分解。

Answer 1

1.x²(y-4)-(y-4)
=(x^2-1)(y-4)
=(x+1)(x-1)(y-4)

2.2x²-32
=2(x^2-16)
=2(x+4)(x-4)

3.已知a+b=8且a²-b²=48.则a-3b=
a+b=8
a^2-b^2=48
(a+b)(a-b)=48
a-b=6

a+b=8
a=8-b

把a=8-b代入a-b=6
8-b-b=6
8-2b=6
b=1
把b=1代入a-b=6
a-1=6
a=7

a-3b=7-3*1=4

4.x²-4y²
=(x+2y)(x-2y)

5.-x²+x²y²
=-x^2(1-y^2)
=-x^2(1+y)(1-y)

6.a²(a-b)+b²(b-a)
=(a^2-b^2)(a-b)
=(a+b)(a-b)^2

7.(a+b)²-(a-b)²
=(a+b+a-b)(a+b-a+b)
=2a(2b)
=4ab

8.4x²-5
题目是否有误？

9.x²-16
=(x+4)(x-4)

10.x^3+x²y-xy²-y^3
=x^2(x+y)-y^2(x+y)
=(x+y)^2(x-y)

11.(5m²+3n²）²-（3m²+5n²）²
=(5m^2+3n^2+3m^2+5n^2)(5m^2+3n^2-3m^2-5n^2)
=(8m^2+8n^2)(2m^2-2n^2)
=8(m^2+n^2)*2(m+n)(m-n)
=16(m+n)(m-n)(m^2+n^2)

Answer 2

1.x²(y-4)-(y-4) =(x²-1)(y-4)=(x+1)(x-1)(y-4)

2.2x²-32 =2(x²-16)=2(x+4)(x-4)

3.已知a+b=8且a²-b²=48.则a-3b= 4
则(a+b)(a-b)=48 a-b=6 a=7 b=1
4.x²-4y² =(x+2y)(x-2y)

5.-x²+x²y² =x²(y²-1)=x²(y+1)(y-1)

6.a²(a-b)+b²(b-a) =(a-b)(a²-b²)=(a-b)²(a+b)

7.(a+b)²-(a-b)²=(a+b+a-b)(a+b-a+b)=4ab

8.4x²-5 =(2x+根号5)(2x-根号5)

9.x²-16 =(x-4)(x+4)

10.x^3+x²y-xy²-y^3 =x²(y+x)-y²(x+y)=(x+y)²(x-y)

11.(5m²+3n²）²-（3m²+5n²）²= (5m²+3n²+3m²+5n²)(5m²+3n²-3m²-5n²)
=16(m²+n²)(m²-n²)=16(m²+n²)(m+n)(m-n)