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2. 先化简后求值：$(x + 1)(x - 3) - (x - 3)(x - 1)$,其中$x = 2$.
答案
2x-6,-2
解析
$(x + 1)(x - 3) - (x - 3)(x - 1)$
$=(x - 3)[(x + 1) - (x - 1)]$
$=(x - 3)(x + 1 - x + 1)$
$=(x - 3)×2$
$=2x - 6$
当$x = 2$时，$2x - 6 = 2×2 - 6 = 4 - 6 = -2$
$=(x - 3)[(x + 1) - (x - 1)]$
$=(x - 3)(x + 1 - x + 1)$
$=(x - 3)×2$
$=2x - 6$
当$x = 2$时，$2x - 6 = 2×2 - 6 = 4 - 6 = -2$
3. (1)计算下列式子：
① $(x + 2)(x + 5) = $
③ $(x + 2)(x - 5) = $
(2)从上面的计算中总结出规律：$(x + a)(x + b) = $
(3)运用上面的规律,直接写出下列各式的结果：
① $(x + 4)(x + 7) = $
③ $(x - 3)(x - 4) = $
① $(x + 2)(x + 5) = $
x²+7x+10
；② $(x - 2)(x - 5) = $x²-7x+10
；③ $(x + 2)(x - 5) = $
x²-3x-10
；④ $(x - 2)(x + 5) = $x²+3x-10
.(2)从上面的计算中总结出规律：$(x + a)(x + b) = $
x²+(a+b)x+ab
,并用多项式的乘法法则进行检验.(3)运用上面的规律,直接写出下列各式的结果：
① $(x + 4)(x + 7) = $
x²+11x+28
；② $(m - 2)(m + 3) = $m²+m-6
；③ $(x - 3)(x - 4) = $
x²-7x+12
；④ $(y - \dfrac{1}{2})(y + \dfrac{1}{3}) = $y²-$\frac{1}{6}$y-$\frac{1}{6}$
.答案
(1)①x²+7x+10 ②x²-7x+10 ③x²-3x-10 ④x²+3x-10
(2)x²+(a+b)x+ab
(3)①x²+11x+28 ②m²+m-6 ③x²-7x+12 ④y²-$\frac{1}{6}$y-$\frac{1}{6}$
