因式分解的练习题(1)4x(a-b)+(b2-a2); (2)(a2+b2)2-4a2b2; (3)x4+2x2-3;
2个回答

(1)4x(a-b)+(b²-a²)

=4x(a-b)-(a-b)(a+b)

=(a-b)(4x-a-b)

(2)(a²+b²)²-4a²b²

=(a²+b²-2ab)(a²+b²+2ab)

=(a-b)²(a+b)²

(3)x^4+2x²-3

=x^4+2x²+1-4

=(x²+1)²-4

=(x²+1-2)(x²+1+2)

=(x²-1)(x²+3)

=(x+1)(x-1)(x²+3)

(4)(x+y)²-3(x+y)

=(x+y)(x+y-3)

(5)x³-2x²-3x

=x(x²-2x-3)

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

(6)4a²-b²+6a-3b

=(4a²-b²)+6a-3b

=(2a-b)(2a+b)+3(2a-b)

=(2a-b)(2a+b+3)