十字相乘法本质是一种简化方程的形式,它能把二次三项式分解因式,但是要务必注意各项系数的符号。十字相乘法的方法简单来讲就是:十字左边相乘等于二次项,右边相乘等于常数项,交叉相乘再相加等于一次项。其实就是运用乘法公式(x+a)(x+b)=x²+(a+b)x+ab的逆运算来进行因式分解。
方法/步骤
明确十字相乘法的概念和核心。
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/9c16fdfaaf51f3dece418b1b84eef01f3b2979d9?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/fcfaaf51f3deb48ff79a93a1e01f3a292cf578d9?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
我们来看一下这个乘法公式(x+a)(x+b),我们很容易解得(x+a)(x+b)=x²+(a+b)x+ab。现在将它逆过来看。
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/8435e5dde71190ef0508a0a0de1b9d16fcfa60d9?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
这样分解出来,结果要怎么写呢?我们继续看x²+(a+b)x+ab的因式分解。
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/e61190ef76c6a7efbbd59a59edfaaf51f2de66d9?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
如果二次项系数不是1,又该怎么分解呢?我们看一下这个例题。
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/d4628535e5dde711e2217189b7efce1b9c1661d9?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
下面我们看一下,十字相乘法在因式分解中的应用。
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/cf1b9d16fdfaaf518a10b3c09c5494eef11f7ad9?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/77c6a7efce1b9d168a34a81ee3deb48f8d5464d9?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
了解一下十字相乘法在解方程中的应用。
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/e4dde71190ef76c6d321c9548d16fdfaae5167d9?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
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十字相乘法进行因式分解可以简化我们的计算,很实用的一种方法。但不是所有的因式分解都可以用十字相乘法,不能盲目使用,我们应该在做题过程中积累经验,尽快判断能否使用这种方法。