(x+1)(x十3)(x十5)(x十7)
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解决时间 2021-01-18 21:20
- 提问者网友：最美的风景
- 2021-01-18 11:24
(x+1)(x十3)(x十5)(x十7)
最佳答案
- 五星知识达人网友：拾荒鲤
- 2021-01-18 11:54
原式=［(X+1)(X+7)］［(X+3)(X+5)］
=［X^2+8X+7］［X^2+8X+8］
=(X^2+8X)^2+15(X^2+8X)+56
=X^4+16X^3+64X^2+15X^2+120X+56
=X^4+16X^3+79X^2+120X+56。
=［X^2+8X+7］［X^2+8X+8］
=(X^2+8X)^2+15(X^2+8X)+56
=X^4+16X^3+64X^2+15X^2+120X+56
=X^4+16X^3+79X^2+120X+56。
全部回答
- 1楼网友：琴狂剑也妄
- 2021-01-18 12:56
(x+1)(x+3)(x+5)(x+7)-9
=(x+1)(x+7)(x+3)(x+5)-9
=(x²+8x+7)(x²+8x+15)-9
=(x²+8x+11-4)(x²+8x+11+4)-9
=(x²+8x+11)²-16-9
=(x²+8x+11)²-5²
=(x²+8x+11+5)(x²+8x+11-5)
=(x²+8x+16)(x²+8x+6)
=(x+4)²(x²+8x+6)
=(x+1)(x+7)(x+3)(x+5)-9
=(x²+8x+7)(x²+8x+15)-9
=(x²+8x+11-4)(x²+8x+11+4)-9
=(x²+8x+11)²-16-9
=(x²+8x+11)²-5²
=(x²+8x+11+5)(x²+8x+11-5)
=(x²+8x+16)(x²+8x+6)
=(x+4)²(x²+8x+6)
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