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(3x^2+2x+1)^2-(2x^2+3x+3)^2(x^2-3)^2-4x^2
题目详情
(3x^2+2x+1)^2-(2x^2+3x+3)^2
(x^2-3)^2-4x^2
(x^2-3)^2-4x^2
▼优质解答
答案和解析
4x^4-20x²y²+16y^4
=4(x^4-5x²y²+4y^4)
=4(x²-y²)(x²-4y²)
=4(x+y)(x-y)(x+2y)(x-2y)
(3x²+2x+1)²-(2x²+3x+3)²
=[(3x²+2x+1)+(2x²+3x+3)][(3x²+2x+1)-(2x²+3x+3)]
=(3x²+2x+1+2x²+3x+3)(3x²+2x+1-2x²-3x-3)
=(5x²+5x+4)(x²-x-2)
=(5x²+5x+4)(x+1)(x-2)
(x²-3)²-4x²
=(x²-3)²-(2x)²
=[(x²-3)+2x][(x²-3)-2x]
=(x²+2x-3)(x²-2x-3)
=(x-1)(x+3)(x+1)(x-3)
=4(x^4-5x²y²+4y^4)
=4(x²-y²)(x²-4y²)
=4(x+y)(x-y)(x+2y)(x-2y)
(3x²+2x+1)²-(2x²+3x+3)²
=[(3x²+2x+1)+(2x²+3x+3)][(3x²+2x+1)-(2x²+3x+3)]
=(3x²+2x+1+2x²+3x+3)(3x²+2x+1-2x²-3x-3)
=(5x²+5x+4)(x²-x-2)
=(5x²+5x+4)(x+1)(x-2)
(x²-3)²-4x²
=(x²-3)²-(2x)²
=[(x²-3)+2x][(x²-3)-2x]
=(x²+2x-3)(x²-2x-3)
=(x-1)(x+3)(x+1)(x-3)
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