Question

请问下列各式怎么分解因式(a+b)^2-a^2. 16-24(x-y)+9(x-y)^2. 4x^2-4x(y-1)+(y-1)^2. 4(x+y)^2-4(x+y)(x

Answer 1

(a+b)^2-a^2=(a+b-a)(a+b+a)=b(2a+b)
16-24(x-y)+9(x-y)^2=4^2-24(x-y)+[3(x-y)]^2=[3(x-y)-2]^2=(3x-3y-2)^2
4x^2-4x(y-1)+(y-1)^2=[2x-(y-1)]^2=(2x-y+1)^2
4(x+y)^2-4(x+y)(x-y)+(x-y)^2=[2(x+y)-(x-y)][2(x+y)+(x-y)]=(x+3y)(3x+y)
祝你学习进步！！！

Answer 2

(a+b)^2-a^2=(a+b-a)(a+b+a)=b(2a+b)
16-24(x-y)+9(x-y)^2=4^2-24(x-y)+[3(x-y)]^2=[3(x-y)-2]^2=(3x-3y-2)^2
4x^2-4x(y-1)+(y-1)^2=[2x-(y-1)]^2=(2x-y+1)^2
4(x+y)^2-4(x+y)(x-y)+(x-y)^2=[2(x+y)-(x-y)][2(x+y)+(x-y)]=(x+3y)(3x+y)

Answer 3

(a+b)^2-a^2=a^2+b^2+2ab-a^2=b^2+2ab=b（b+2a）
16-24(x-y)+9(x-y)^2=（3(x-y)-4）^2=（3x-3y-4）^2
4x^2-4x(y-1)+(y-1)^2=（2x-y+1））^2
4(x+y)^2-4(x+y)(x-y）=4(x+y)（4x+4y-4x+4y）=32(x+y)y

Answer 4

(a+b)^2-a^2=（2a+b）*b
16-24(x-y)+9(x-y)^2=（3x-3y-4）^2
4x^2-4x(y-1)+(y-1)^2=(2x-y+1)^2