Question

因式分解！！！！~谢谢！~急急急~！

1、P^2-pq+1/4q^2
2、-x^2+14xy-49y^2
3、x^4-8x^2y^2+16y^4
4、x^4+4x^2+4

Answer 1

1、P^2-pq+1/4q^2
=(p-1/2q)(^2)
2、-x^2+14xy-49y^2
=-(x-7y)(^2)
3、x^4-8x^2y^2+16y^4
=(x²-4y²)(^2)
=[(x+2y)(x-2y)](^2)
4、x^4+4x^2+4
=(x²+2)(^2)
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Answer 2

1、P²-pq+1/4q²=（p-1/2q)²
2、-x²+14xy-49y²=-(x²-14xy+49y²)=-(x-7y)²
3、x^4-8x^2y^2+16y^4
=(x²)²-8x²y²+(4y²)²
=(x²-4y²)²
=(x+2y)²(x-2y)²
4、x^4+4x^2+4
=(x²)²+4x²+2²
=(x²+2)²

追问

1、P²-pq+1/4q²
=（p-1/2q)²
2、-x²+14xy-49y²
=-(x²-14xy+49y²)
=-(x-7y)²
3、x^4-8x^2y^2+16y^4
=(x²)²-8x²y²+(4y²)²
=(x²-4y²)²
=(x+2y)²(x-2y)²
4、x^4+4x^2+4
=(x²)²+4x²+2²
=(x²+2)²

Answer 3

1、P^2-pq+1/4q^2
=(p-1/2q)²
2、-x^2+14xy-49y^2
=-（x-7y）²
3、x^4-8x^2y^2+16y^4
=（x²-4y)²
=(x+2y)²(x-2y)²
4、x^4+4x^2+4
=(x+2)²

Answer 4

(p-1/2q)^2
-(x-7y)^2
(x+2y)^2*(x-2y)^2
（x^2+2)^2