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
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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
(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
![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](/uploads/image/z/953090-26-0.jpg?t=%E5%88%A9%E7%94%A8%E4%B9%98%E6%B3%95%E5%85%AC%E5%BC%8F%E8%AE%A1%E7%AE%97%28x%2By%29%28x%26sup2%3B%2By%26sup2%3B%EF%BC%89%EF%BC%88x-y%29%28x%E7%9A%84%E5%9B%9B%E6%AC%A1%E6%96%B9%2By%E5%9B%9B%E6%AC%A1%E6%96%B9%29%EF%BC%88a-2b%2B3%29%28a%2B2b)
(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
= (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
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