Question

初二数学题 因式分解

因式分解
-10x²y-5xy²+15xy
-8a^(m)b^3+12a^(m+1)b^2
x(x-y)a_b)-y(y-x)(b-a)
xy(x-y)-x(y-x)²
-1+16m^4
(2x-3y)²-4x
1/4+a²+a^4
a^4-8a²b²+16b^4
49(m+n)²-16(m-n)²
(a+b+c+d)²-(a-b+c-d)²

Answer 1

-10x²y-5xy²+15xy
=-5xy(2x+5y-3)
-8a^(m)b^3+12a^(m+1)b^2
=-4a^(m)b^2(2b-3a)
x(x-y)a_b)-y(y-x)(b-a)
=(x-y)(a-b)(x+y)
xy(x-y)-x(y-x)²
=x(x-y)(y-x+y)
=x(x-y)(2y-x)
-1+16m^4
=(4m^2+1)(4m^2-1)
=(4m^2+1)(2m+1)(2m-1)

(2x-3y)²-4x
题目有误，不能分解
1/4+a²+a^4
=a^2(1/4a^2+1+a^2)
=a^2(1/2a+a)^2

a^4-8a²b²+16b^4
=(a^2-4b^2)^2
=(a+2b)^2(a-2b)^2

49(m+n)²-16(m-n)²
=(7(m+n)+4(m-n))(7(m+n)-4(m-n))
=(11m+3n)(3m+11n)

(a+b+c+d)²-(a-b+c-d)²
=((a+b+c+d+(a-b+c-d))((a+b+c+d-(a-b+c-d))
=(2a+2c)(2b+2d)
=4(a+c)(b+d)

追问

(2x-3y)²-4x²

追答

(2x-3y)2-4x2
=(2x-3y+2x)(2x-3y-2x)
=-3y(4x-3y)

Answer 2

（1）=-5xy（2x+y-3）=-5xy（x-1）（2x+3）

Answer 3

10x²y-5xy²+15xy=5xy(2x-y+3)

-8a^(m)b^3+12a^(m+1)b^2=-4a^(m)b²(2b-3a)

x(x-y)(a-b)-y(y-x)(b-a)=x(x-y)(a-b)-y(x-y)(a-b)=(x-y)(a-b)(x-y)=(a-b)(x-y)²

xy(x-y)-x(y-x)²=x(x-y)(y-x-y)=-x²(x-y)

-1+16m^4=(4m²-1)(4m²+1)=(2m-1)(2m+1)(4m²+1)

(2x-3y)²-4x²=(2x-3y-2x)(2x-3y+2x)=-3y(4x-3y)

1/4+a²+a^4=(1/2+a²)²

a^4-8a²b²+16b^4=(a²-4b²)²=(a-2b)²(a+2b)²

49(m+n)²-16(m-n)²=[7(m+n)-4(m-n)][7(m+n)+4(m-n)]=(7m+7n-4m+4n)(7m+7n+4m-4n)
=(3m+11n)(11m+3n)

(a+b+c+d)²-(a-b+c-d)²=(a+b+c+d-a+b-c+d)(a+b+c+d+a-b+c-d)=(2b+2d)(2a+2c)=4(b+d)(a+c)

Answer 4

-10x²y-5xy²+15xy
=5xy(-2x-y+3)

-8a^(m)b^3+12a^(m+1)b^2
=4a^(m)b^2(3a-2b)

x(x-y)a_b)-y(y-x)(b-a)
=(x-y)(a-b)(x-y)=(x-y)²(a-b)

xy(x-y)-x(y-x)²
=x(x-y)(y-(x-y))=x(x-y)(2y-x)

-1+16m^4
=(4m²)²-1=(4m²+1)(4m²-1)=(4m²+1)(2m+1)(2m-1)

(2x-3y)²-4x²
=(2x-3y+2x)(2x-3y-2x)=(4x-3y)(-3y)=3y(3y-4x)

1/4+a²+a^4
=(a²+1/2)²

a^4-8a²b²+16b^4
=(a²-4b²)²=[(a+2b)(a-2b)]²

49(m+n)²-16(m-n)²
=[7(m+n)+4(m-n)][7(m+n)-4(m-n)]=(11m+3n)(3m+11n)

(a+b+c+d)²-(a-b+c-d)²
=(a+b+c+d+a+c-b-d)(a+b+c+d-a-c+b+d)=4(a+c)(b+d)