Question

分解因式：①2x^5-8x^3②3a^3-18a^2+27a③2x^2-8x-10④x^4+3x^2-28⑤(x^2-2x)^2+2(x^2-2x)-15

⑥a^2-3a+ab-3b⑦1-a^2-2ab-b^2

Answer 1

①2x^5-8x^3
=2x³(x²-4)
=2x³(x+2)(x-2)

②3a^3-18a^2+27a
=3a(a²-6a+9)
=3a(a-3)²

③2x^2-8x-10
=2(x²-4x-5)
=2(x-5)(x+1)

④x^4+3x^2-28
=(x²+7)(x²-4)
=(x²+7)(x+2)(x-2)

⑤(x^2-2x)^2+2(x^2-2x)-15
=(x²-2x+5)(x²-2x-3)
=(x²-2x+5)(x-3)(x+1)

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

⑦1-a^2-2ab-b^2
=1-(a²+2ab+b²)
=1-(a+b)²
=(1+a+b)(1-a-b)

Answer 2

①=2x³(x+2)(x-2)
②=3a(a-3)²
③=2(x-5)(x+1)
④=(x²+7)(x+2)(x-2)
⑤=(x²-2x+5)(x-3)(x+1)
⑥=(a-3)(a+b)
⑦=(1+a+b)(1-a-b)