Question

计算啦 ~分解因式 a’‘-b’‘+2b-1 a’‘b’‘-a’‘+2ab+1 (x+y)''-4(x+y-1)。。。。

a’‘-b’‘+2b-1 a’‘b’‘-a’‘+2ab+1 (x+y)''-4(x+y-1)
(x''-x)''-8x''+8x+12 (1+a'')(1+b'')-4ab 8(2x-y)''-18(3x+2y)''
(x-1)(x-2)(x-3)(x-4)-48 (ay+by)''+(by-ay)'' (x''-3x)''-(2x''-6x)(x-1)+(x-4)''
分解因式 ，会几题就拜托啦~
''是平方的意思

Answer 1

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

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

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

(x^2-x)^2-8x^2+8x+12
=(x^2-x)^2-8(x^2-x)+12
=(x^2-x-2)(x^2-x-6)
=(x-2)(x+1)(x-3)(x+2)

(1+a^2)(1+b^2)-4ab(原题有误 ）

(1-a^2)(1-b^2)-4ab
=1-a^2-b^2+a^2b^2-4ab
=(1-2ab+a^2b^2)-(a^2+b^2-2ab)
=(1-ab)^2-(a-b)^2
=(1-ab+a-b)(1-ab-a+b)

8(2x-y)^2-18(3x+2y)^2
=2[4(2x-y)^2-9(3x+2y)^2]
=2[(2x-y)-3(3x+2y)][(2x-y)+3(3x+2y)]
=2(2x-y-9x-6y)(2x-y+9x+6y)
=2(-7x-7y)(11x+5y)
=-14(x+y(11x+5y)

(x-1)(x-2)(x-3)(x-4)-48
=(x-1)(x-4)(x-2)(x-3)-48
=(x^2-5x+4)(x^2-5x+6)-48
=(x^2-5x)^2+10(x^2-5x+6）-24
=(x^2-5x-2)(x^2-5x+12）

(ay+by)^2+(by-ay)^2
=[y(a+b)]^2+[y(a-b)]^2
=y^2(a+b)^2+y^2(a-b)^2
=y^2[(a+b)^2+(a-b)^2]
=y^2[a^2+2ab+b^2+a^2-2ab+b^2]
=y^2(2a^2+2b^2)
=2y^2(a^2+b^2)

(x^2-3x)^2-(2x^2-6x)(x-4)+(x-4)^2
=(x^2-3x)^2-2(x^2-3x)(x-4)+(x-4)^2
=[(x^2-3x)-(x-4)]^2
=[x^2-3x-x+4]^2
=[x^2-4x+4]^2
=[(x-2)^2]^2
=(x-2)^4