几道分解因式,写出详细过程

来源:百度知道 编辑:UC知道 时间:2024/09/24 22:53:31
1.(a-b)(x-y)-(b-a)(x+y)

2.x(p-q)-y(p-q)+z(q-p)

3.p^2(p+q)^2-q^2(p-q)^2

4.(1/2 x+2/3 y-3/4 z)^2-(1/2 x-2/3 y-3/4z)^2

1.
(a-b)(x-y)-(b-a)(x+y)
=(a-b)(x-y)+(a-b)(x+y)
=(a-b)[(x-y)+(x+y)]
=2x(a-b)

2.
x(p-q)-y(p-q)+z(q-p)
=x(p-q)-y(p-q)-z(p-q)
=(p-q)(x-y-z)

3.
p^2(p+q)^2-q^2(p-q)^2
=[p(p+q)-q(p-q)][p(p+q)+q(p-q)]
=[(p^2+pq)-(pq-q^2)][(p^2+pq)+(pq-q^2)]
=(p^2+pq-pq+q^2)(p^2+pq+pq-q^2)
=(p^2+q^2)(p^2+2pq-q^2)

4.
(1/2x+2/3y-3/4z)^2-(1/2x-2/3y-3/4z)^2
=[(1/2x+2/3y-3/4z)-(1/2x-2/3y-3/4z)]
[(1/2x+2/3y-3/4z)+(1/2x-2/3y-3/4z)]
=(1/2x+2/3y-3/4z-1/2x+2/3y+3/4z)(1/2x+2/3y-3/4z+1/2x-2/3y-3/4z)
=(2/3y+2/3y)(x-3/2z)
=(4/3y)(x-3/2z)

1.(a-b)(x-y)-(b-a)(x+y)
=(a-b)(x-y+x+y)
=2x(a-b)
2.x(p-q)-y(p-q)+z(q-p)
=(p-q)(x-y-z)

3.p^2(p+q)^2-q^2(p-q)^2
=

4.(1/2 x+2/3 y-3/4 z)^2-(1/2 x-2/3 y-3/4z)^2
=

1.(a-b)(x-y)-(b-a)(x+y)
=(a-b)(x-y+x+y)
=2x(a-b)
2.x(p-q)-y(p-q)+z(q-p)
=(p-q)(x-y-z)

3.p^2(p+q)^2-q^2(p-q)^2