急需因式分解(完全平方公式和平方差公式的)、整式计算题,(题量一定要多)要有答案。谢谢各位了

"^"是什么意思
2024-12-12 17:57:56
推荐回答(1个)
回答1:

分解因式:
1‘3a(a-b)(a+b)-6(b-a)^2
2‘x^4-y^4
3‘4(a+2b)^2-9(a-2b)^2
4‘(x+y)^2+x+y
5‘(x^2-7x+6)(x^2-x-6)+56
6‘x^3+x-2
7‘X^2-4Y^2-X+2Y

3a(a-b)(a+b)-6(b-a)^2
=3a(a-b)(a+b)-6(a-b)^2
=(a-b)(3a^2+3ab-6a+6b)
=3(a-b)(a^2+ab-2a+2b)

x^4-y^4
=(x^2+y^2)(x^2-y^2)
=(x^2+y^2)(x+y)(x-y)

4(a+2b)^2-9(a-2b)^2
=(2a+4b)^2-(3a-6b)^2
=(5a-2b)(10b-a)

(x+y)^2+x+y
=(x+y)^2+(x+y)
=(x+y)(x+y+1)

(x^2-7x+6)(x^2-x-6)+56
=(x-1)(x-6)(x-3)(x+2)+56
=[(x+2)(x-6)][(x-1)(x-3)]+56
=(x^2-4x+3-15)(x^2-4x+3)+56
=[(x^2-4x+3)]^2-15(x^2-4x+3)+56
=(x^2-4x+3-7)(x^2-4x+3-8)
=(x^2-4x-4)(x^2-4x-5)
=(x^2-4x-4)(x-5)(x+1)

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

X^2-4Y^2-X+2Y
=X^2-(2Y)^2-X+2Y
=(X-2Y)(X+2Y)-(X-2Y)
=(X-2Y)(X+2Y-1)