Question

2(a+b)²+(a+b)(a-b)-6(a-b)²

用十字相乘法做

Answer 1

把a+b看做m a-b看做n
则有2m²+mn-6n²
利用十字相乘得出： (2m-3n)(m+2n)
带入得：[2(a+b)-3(a-b)]×[(a+b)+2(a-b)]
化简得(5b-a)(3a-b)

Answer 2

法1：2(a+b)²+(a+b)(a-b)-6(a-b)²
=2(a²+2ab+b²)+(a²-b²)-6(a²-2ab+b²)
=2a²+4ab+2b²+a²-b²-6a²+12ab-6b²
=-3a²+16ab-5b²
=-(3a-b)(a-5b)
法2：2(a+b)²+(a+b)(a-b)-6(a-b)²
=[2(a+b)-3(a-b)][(a+b)+2(a-b)]
=(-a+5b)(3a-b)
=-(3a-b)(a-5b)