Question

运用平方差公式分解因式

1. x^2-9y^2
2. 36-25x^2
3. x^2y-xy^2
4. mn^2-m
5 2x^3-8x
6. 2x^3-8x
7. ax^2-ay^2
8.2x^3y-2xy^3

Answer 1

1. x^2-9y^2=(x-3y)(x+3y)

2. 36-25x^2=(6-5x)(6+5x)

3. x^2y-xy^2=xy(x-y)

4. mn^2-m =m(n²-1)=m(n-1)(n+1)

5 2x^3-8x=2x(x²-4)=2x(x-2)(x+2)

6. 2x^3-8x=2x(x²-4)=2x(x-2)(x+2)

7. ax^2-ay^2=a(x²-y²)=a(x-y)(x+y)

8.2x^3y-2xy^3=2xy(x²-y²)=2xy(x-y)(x+y)

Answer 2

1. x^2-9y^2
=(x-3y)(x+3y)

2. 36-25x^2
=(6-5x)(6+5x)

3. x^2y-xy^2
=xy(x-y)

4. mn^2-m
=m(n^2-1)
=m(n+1)(n-1)

5 2x^3-8x
=2x(x^2-4)
=2x(x+2)(x-2)

6. 2x^3-8x
=2x(x^2-4)
=2x(x+2)(x-2)

7. ax^2-ay^2
=a(x^2-y^2)
=a(x+y)(x-y)

8.2x^3y-2xy^3
=2xy(x^2-y^2)
=2xy(x+y)(x-y)

Answer 3

1.(X-3Y)(X+3Y)
2.(6-5X)(6+5X)
3.(X-Y）XY
4.M(N-1)(N+1)
5.6.2X(X-1)(X+1)
7.A(X-Y)(X+Y)
8.2XY(X-Y)(X+Y)

Answer 4

2x3y-ay2