(x−2)(x−6)left parenthesis, x, minus, 2, right parenthesis, left parenthesis, x, minus, 6, right parenthesis
应用乘法分配律.
=(x−2)(x−6)x(x−6)−2(x−6)
再次应用乘法分配律.
=x(x)+x(−6)−2(x)−2(−6)equals, start color #11accd, x, end color #11accd, left parenthesis, x, right parenthesis, plus, start color #11accd, x, end color #11accd, left parenthesis, minus, 6, right parenthesis, start color #11accd, minus, 2, end color #11accd, left parenthesis, x, right parenthesis, start color #11accd, minus, 2, end color #11accd, left parenthesis, minus, 6, right parenthesis
注意规律。我们用第一个二项式中的每一项去乘以第二个二项式中的每一项。
简化.
==x2−6x−2x+12x2−8x+12
例题 2
展开表达式.
(−a+1)(5a+6)left parenthesis, minus, a, plus, 1, right parenthesis, left parenthesis, 5, a, plus, 6, right parenthesis
应用乘法分配律.
=(−a+1)(5a+6)−a(5a+6)+1(5a+6)
再次应用乘法分配律.
=−a(5a)−a(6)+1(5a)+1(6)equals, start color #7854ab, minus, a, end color #7854ab, left parenthesis, 5, a, right parenthesis, start color #7854ab, minus, a, end color #7854ab, left parenthesis, 6, right parenthesis, plus, start color #7854ab, 1, end color #7854ab, left parenthesis, 5, a, right parenthesis, plus, start color #7854ab, 1, end color #7854ab, left parenthesis, 6, right parenthesis