Question

已知a+b=-2,ab=-3,求a(a平方-b平方)-a(a+b)平方的值

过程要详细而且正确！！速度！速度！

Answer 1

a(a² - b²) - a(a + b)²
= a(a + b)(a - b) - a(a + b)(a + b)
= a (a + b)(a - b - a - b)
= -2ab(a + b)
= -2 × (-3) × (-2)
= -12

追问

为什么变成a (a + b)(a - b - a - b)，有点不懂

追答

a(a + b)(a - b) - a(a + b)(a + b)
提取公因式 a(a + b)，
得到 a(a + b) [(a - b) - (a + b)]
去括号，得到 a (a + b)(a - b - a - b)

追问

懂了！！Thanks！！

追答

不客气

Answer 2

a^2-b^2=(a+b)(a-b)=-2(a-b)
故原式可以化作:-2a(a-b)+2a(a+b)
=4ab=-12

Answer 3

=a(a^2-b^2-a^2-b^2-2ab)
=a(-2b^2-2ab)
=-2ab(a+b)
=-12