Question

分解因式

1.（a+b）^2+2(a+b)c+c^2 2.4a(a-b)+b^2 3.4xy^2-4x^2y-y^3 4.(4a^2+1)^2-16a^2 5.5x^2-20 6.64-16a+a^2 7.2(x-y)-ax+ay 8. 0.49x^2-0.04y^2 9.-4a^2b^2+4ab-1 10.(m-n)^3+2n(n-m)^2 11.3ax^3+12ax^3 12.1/2a^3b+2a^2b^2+2ab^3

Answer 1

1.（a+b）^2+2(a+b)c+c^2 =（a+b+c）^2
2.4a(a-b)+b^2 =4a^2-4ab+b^2=(2a-b)^2
3.4xy^2-4x^2y-y^3=-y(-4xy+4x^2+y^2)=-y(2x-y)^2
4.(4a^2+1)^2-16a^2=(4a^2+1+4a)(4a^2+1-4a)=(2a+1)^2(2a-1)^2
5.5x^2-20=5(x^2-4)=5(x-2)(x+2)
6.64-16a+a^2=(8-a)^2
7.2(x-y)-ax+ay=2x-2y-ax+ay=(2-a)x+y(a-2)=(2-a)(x-y)
8. 0.49x^2-0.04y^2=(0.7x-0.2y)(0.7x+0.2y)
9.-4a^2b^2+4ab-1 =-[(2ab)^2-4ab+1 ]=-(2ab-1)^2
10.(m-n)^3+2n(n-m)^2=(m-n)^3+2n(m-n)^2=(m-n)^2(m-n+2n)=(m-n)^2(m+n) 11.3ax^3+12ax^3 =15ax^3
12.1/2a^3b+2a^2b^2+2ab^3=1/2ab(a^2+4ab+4b^2)=1/2ab(a+2b)^2