Question

因式分解 1.（x+p)^2-(x+y)^2 2.36(x+y)^2-49(x-y)^2 3.(x^2+x+1)^2-1

Answer 1

1.（x+p)^2-(x+y)^2
=(x+p+x+y)(x+p-x-y)
=(2x+p+y)(p-y)

2.36(x+y)^2-49(x-y)^2
=[6(x+y)-7(x-y)][6(x+y)+7(x-y)]
=(-x+13y)(13x-y)
=-(x-13y)(13x-y)

3.(x^2+x+1)^2-1
=(x²+x+2)(x²+x)
=x(x+1)(x²+x+2)

Answer 2

1.（x+p)^2-(x+y)^2
=(2x+y+p)(p-y)

2. 36(x+y)^2-49(x-y)^2
=(6x+6y+7x-7y)(6x+6y-7x+7y)
=(13x-y)(13y-x)

3 .(x^2+x+1)^2-1
=(x^2+x+2)(x^2+x)

Answer 3

1. （2x+y+p)(p-y）
2.（13y-x)(13x-y）
3. x(x^2+x+2)(x+1)

Answer 4

1、(2x+p+y)(p-y)
2、-13(x-y)^2
3、x(x^2+x+2)(x+1)

Answer 5

1、平方差公式 （x+p）^2-(x+y)^2=(x+p+x+y)(x+p-x-y)=(2x+p+y)(p-y)
2、平方差公式 36(x+y)^2-49(x-y)^2=(6x+6y)^2-(7x-7y)^2=(6x+6y+7x-7y)(6x+6y-7x+7y)
=(13x-y)(13y-x)
3、平方差公式 (x^2+x+1)^2-1=(x^2+x+1)^2-1^2=(x^2+x+1-1)(x^2+x+1+1)=(x^2+x)(x^2+x+2)
=x(x+1)(x^2+x+2)