因式分解7.（a+b）（x+y）-（b+a）（y-x）8.144（a-b）ˇ2-225（a+b）ˇ29.aˇ2bˇ2+4-4ab10.aˇ3-2aˇ2b+abˇ211.xyˇ2-4xˇ2-16分之1yˇ412.（mˇ2+2m）ˇ2-（2m+4nˇ2）ˇ2

Question

因式分解
7.（a+b）（x+y）-（b+a）（y-x）
8.144（a-b）ˇ2-225（a+b）ˇ2
9.aˇ2 bˇ2+4-4ab
10.aˇ3-2aˇ2b+abˇ2
11.xyˇ2-4xˇ2-16分之1yˇ4
12.（mˇ2+2m）ˇ2-（2m+4nˇ2）ˇ2

Answer 1

7.(a+b)(x+y)-(b+a)(y-x)
=(a+b)(x+y)-(a+b)(y-x)
=(a+b)((x+y)-(y-x))
=(a+b)(x+y-y+x)
=2x(a+b)
8.144(a-b)^2-225(a+b)^2
=(12(a-b))^2-(15(a+b))^2
=(12(a-b)-15(a+b))(12(a-b)+15(a+b))
=(12a-12b-15a-15b)(12a-12b+15a+15b)
=(-3a-27b)(27a+3b)
=(-3)(a+9b)(3)(9a+b)
=(-9)(a+9b)(9a+b)
=(-9)(9a^2+81ab+ab+9b^2)
=(-9)(9a^2+82ab+9b^2)
=-81a^2-738ab-81b^2
9.a^2b^2+4-4ab
=(ab)^2-4ab+4
=(ab-2)^2
10.a^3-2a^2b+ab^2
=a(a^2-2ab+b^2)
=2(a-b)^2
11.xy^2-4x^2-(1/16)y^4
=xy^2-(2/16)y^4-4x^2+(1/16)y^4
=(xy^2-(1/8)y^4)-(4x^2-(1/16)y^4)
=y^2(x-(y^2)/8)-(2x-(y^2)/4)(2x+(y^2)/4)
12.(m^2+2m)^2-(2m+4n^2)^2
=((m^2+2m)+(2m+4n^2))((m^2+2m)-(2m+4n^2))
=(m^2+2m+2m+4n^2)(m^2+2m-2m-4n^2)
=(m^2+4m+4n^2)(m^2-4n^2)
=(m^2+4m+4n^2)(m+2n)(m-2n)