Question

多项式的分解因式1、 (2a-b)^2+8ab2、 (a-b)^2+4ab3、 (p-4)(p+1)+3p4、 ab(c

Answer 1

1、 (2a-b)^2+8ab

=4a^2-4ab+b^2+8ab

=4a^2+4ab+b^2

=(2a+b)^2

2、 (a-b)^2+4ab

=a^2-2ab+b^2

=a^2+2ab+b^2

=(a+b)^2

3、 (p-4)(p+1)+3p

=p^2-3p-4+3p

=p^2-4

=(p+2)(p-2)

4、 ab(c^2-d^2)-(a^2-b^2)cd

=abc^2-abd^2-a^2cd+b^2cd

=ac(bc-ad)-bd(ad-bc)

=(bc-ad)(bd-ac)

5、 2(x^2-3ab)+x(4a-3b)

=2x^2-6ab+4ax-3bx

=x(2x-3)+2a(2x-3)

=(2x-3)(x+2a)

6、 a(1-b)^2-1+2b-b^2

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

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

7、 x(x+z)-y(y+z)

=x^2+xz-y^2-yz

=(x+y)(x-y)+z(z-y)

=(x+y+z)(x-y)