Question

因式分解

（1）x的三次方+3x的平方-4x-12=
（2）若多项式5x的平方+7x+a有因式(x+1).则此多项式可以分解为
（3）a的平方b的平方-a的平方-b的平方+1=
（4）(1-x的平方）（1-y的平方）-4xy=
（5）（a-1)(a-2b-1)+b的平方=
（6）x的平方-y的平方-6x+9=
（7）4x的平方+1/4-2x-9y的平方=
快点呀！我给各位大侠磕头了！

Answer 1

（1）x的三次方+3x的平方-4x-12
=x²(x+3)-4(x+3)
=(x²-4)(x+3)
=(x+2)(x-2)(x+3)
（2）若多项式5x的平方+7x+a有因式(x+1).则此多项式可以分解为(x+1)(5x+12)
（3）a的平方b的平方-a的平方-b的平方+1
=a²(b²-1)-(b²-1)
=(a²-1)(b²-1)
=(a+1)(a-1)(b+1)(b-1)
（4）(1-x的平方）（1-y的平方）-4xy=
=1-x²-y²+x²y²-4xy
=1-2xy+x²y²-x²-y²-2xy
=(1-xy)²-(x+y)²
=(1-xy+x+y)(1-xy-x-y)
（5）（a-1)(a-2b-1)+b的平方=
=(a-1)²-2b(a-1)+b²
=(a-1-b)²
（6）x的平方-y的平方-6x+9
=x²-6x+9-y²
=(x-3)²-y²
=(x-3+y)(x-3-y)
（7）4x的平方+1/4-2x-9y的平方=
=1/4(16x²+1-8x)-9y²
=1/4(4x-1)²-9y²
=(2x-1/2)²-(3y)²
=(2x-1/2+3y)(2x-1/2-3y)

Answer 2

x^3+3x^2-4x-12
=x^3-4x+3x^2-12
=x(x^2-4)+3(x^2-4)
=(x^2-4)(x+3)
=(x+2)(x-2)(x+3)

5x^2+7x+a
=(x+1)(5x+a)

a^2b^2-a^2-b^2+1
=a^2(b^2-1)-(b^2-1)
=(a^2-1)(b^2-1)
=(a-1)(a+1)(b-1)(b+1)

(1-x^2)(1-y^2)-4xy
=x^2y^2-x^2-y^2+1-4xy
=x^2y^2-2xy+1-x^2-y^2-2xy
=(xy-1)^2-(x+y)^2
=(xy-1+x+y)(xy-1-x-y)

(a-1)(a-2b-1)+b^2
=(a-1)[(a-1)-2b]+b^2
=(a-1)^2-2b(a-1)+b^2
=(a-1-b)^2

x^2-y^2-6x+9
=x^2-6x+9-y^2
=(x-3)^2-y^2
=(x-3-y)(x-3+y)

4x^2+1/4-2x-9y^2
=4x^2-2x+1/4-9y^2
=(2x-1/2)^2-9y^2
=(2x-1/2+3y)(2x-1/2-3y)

Answer 3

(1) (x-2)*(x+2)*(x+3)
(2) (x+1)*(5x+2)
(3) (b-1)*(b+1)*(a-1)*(a+1)
(4) (x*y+y-1+x)*(-y+x*y-x-1)
(5) (a-b-1)^2
(6) (x-3+y)*(x-3-y)
(7) 1/4*(4*x-1+6*y)*(4*x-1-6*y)

Answer 4

(x+3)(x+2)(x-2)
5(x+1)(x+2/5)
(a+1)(a-1)(b+1)(b-1)
(xy+x+y-1)(xy-x-y-1)
(a-b-1)^2
(x+y-3)(x-y-3)
(2x+3y+1/2)(2x-3y+1/2)