Question

利用乘法公式计算

(x+y)(x²+y²）（x-y)(x的四次方+y四次方)
（a-2b+3)(a+2b-3)
[(x-y)²+(x+y)²](x²-y²)
(m-n-3)²

先化简，再求值
[(a-1/2)²-(a+1/2)²](a+3),其中a=-2

Answer 1

(x+y)(x²+y²）（x-y)(x的四次方+y四次方)
= (x + y)(x - y)(x^2 + y^2)(x^4 + y^4)
= (x^2 - y^2)(x^2 + y^2)(x^4 + y^4)
= (x^4 - y^4)(x^4 + y^4)
= x^8 - y^8

（a-2b+3)(a+2b-3)
= [a - (2b - 3)][a + (2b - 3)]
= a^2 - (2b - 3)^2
= a^2 - 4 b^2 + 12 b - 9

[(x-y)²+(x+y)²](x²-y²)
= 2 (x^2 + y^2)(x^2 - y^2)
= 2 (x^4 - y^4)
= 2 x^4 - 2 y^4

(m-n-3)²
= m^2 + n^2 + 9 - 2 m n - 6 m + 6n

[(a-1/2)²-(a+1/2)²](a+3)
= [(a - 1/2)+(a + 1/2)][(a - 1/2)-(a + 1/2)](a + 3)
= 2 a (-1) (a + 3)
= - 2 a^2 - 6 a
将 a = -2 代入，得
[(a-1/2)²-(a+1/2)²](a+3)
= -2 * （-2）^2 - 6 * （-2）
= 4