Question

几道数学题，要用因式分解的方法，先展开再分解，要过程哦~~

1.（2a-b）^2+8ab
2.(a-b)^2+4ab
3.(p-4)(p+1)+3p
4.ab(c^2 - d^2)-(a^2 - b^2)cd
5.2(x^2 -3ab)+x(4a-3b)
6.a(a-b)^2-1+2b-b^2
7.x(x+z)-y(y+z)

一定要写清过程哦，今天就需要答案，就在线等~~

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+4ab
=a^2+2ab+b^2
=(a+b)^2
3.(p-4)(p+1)+3p
=p^2+p-4p-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
=abc^2+b^2cd-(abd^2+a^2cd)
=bc(ac+bd)-ad(bd+ac)
=(bc-ad)(ac+bd)
5.2(x^2 -3ab)+x(4a-3b)
=2x^2-6ab+4ax-3bx
=2x^2+x(4a-3b)-6ab
=(2x-3b)(x+2a)
6.若为(a-b)^2-1+2b-b^2
=(a-b)^2-(1-2b+b^2)
=(a-b)^2-(b^2-2b+1)
=(a-b)^2-(b-1)^2
=(a-b+b-1)(a-b-b+1)
=(a-1)(a-2b+1)
7.x(x+z)-y(y+z)
=x^2+xz-y^2-yz
=(x^2-y^2)+(xz-yz)
=(x+y)(x-y)+z(x-y)
=(x-y)(x+y+z)