(1)16x的4次方-72x²+81(2)3(a的4次方+a²b²+b的4次方)-9a²b²(3)24a²b²(1)16x的4次方-72x²+81(2)3(a的4次方+a²b²+b的4次方)-9a²b²(3)24a²b²-6(a²+b²)²
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![(1)16x的4次方-72x²+81(2)3(a的4次方+a²b²+b的4次方)-9a²b²(3)24a²b²(1)16x的4次方-72x²+81(2)3(a的4次方+a²b²+b的4次方)-9a²b²(3)24a²b²-6(a²+b²)²](/uploads/image/z/374313-57-3.jpg?t=%281%2916x%E7%9A%844%E6%AC%A1%E6%96%B9-72x%26sup2%3B%2B81%282%293%28a%E7%9A%844%E6%AC%A1%E6%96%B9%2Ba%26sup2%3Bb%26sup2%3B%2Bb%E7%9A%844%E6%AC%A1%E6%96%B9%29-9a%26sup2%3Bb%26sup2%3B%283%2924a%26sup2%3Bb%26sup2%EF%BC%881%EF%BC%8916x%E7%9A%844%E6%AC%A1%E6%96%B9-72x%26%23178%3B%2B81%282%293%28a%E7%9A%844%E6%AC%A1%E6%96%B9%2Ba%26%23178%3Bb%26%23178%3B%2Bb%E7%9A%844%E6%AC%A1%E6%96%B9%EF%BC%89-9a%26%23178%3Bb%26%23178%3B%283%2924a%26%23178%3Bb%26%23178%3B-6%EF%BC%88a%26%23178%3B%2Bb%26%23178%3B%EF%BC%89%26%23178%3B)
(1)16x的4次方-72x²+81(2)3(a的4次方+a²b²+b的4次方)-9a²b²(3)24a²b²(1)16x的4次方-72x²+81(2)3(a的4次方+a²b²+b的4次方)-9a²b²(3)24a²b²-6(a²+b²)²
(1)16x的4次方-72x²+81(2)3(a的4次方+a²b²+b的4次方)-9a²b²(3)24a²b²
(1)16x的4次方-72x²+81(2)3(a的4次方+a²b²+b的4次方)-9a²b²(3)24a²b²-6(a²+b²)²(4)9(x+1)²(x-1)²-6(x²-1)y+y²(5)2(a²+b²)(a+b)²-(a²-b²)²
(1)16x的4次方-72x²+81(2)3(a的4次方+a²b²+b的4次方)-9a²b²(3)24a²b²(1)16x的4次方-72x²+81(2)3(a的4次方+a²b²+b的4次方)-9a²b²(3)24a²b²-6(a²+b²)²
(1)16x的4次方-72x²+81
=(16x²-9)²
=(4x+3)²(4x-3)²
(2)3(a的4次方+a²b²+b的4次方)-9a²b²
=3a的4次方-6a²b²+3b的4次方
=3(a的4次方-2a²b²+b的4次方)
=3(a²-b²)²
=3(a+b)²(a-b)²
(3)24a²b²-6(a²+b²)²
=6[4a²b²-(a²+b²)²]
=6(2ab-a²-b²)(2ab+a²+b²)
=-6(a-b)²(a+b)²
(4)9(x-1)²-6(x²-1)y+y²
=(x-1)²(9-6y+y²)
=(x-1)²(y-3)²
(5)2(a²+b²)(a+b)²-(a²-b²)²
=2(a²+b²)(a+b)²-(a+b)²(a-b)²
=(a+b)²[2(a²+b²)-(a-b)²]
=(a+b)²[a²+b²+2ab]
=(a+b)²(a+b)²
=(a+b)的4次方
解
(1)16x^4-72x²+81
=(4x²)²-2×4x×9+9²
=(4x²-9)²
=(2x-3)²(2x+3)²
(2)3(a^4+a²b²+b^4)-9a²b²
=3(a^4+b^4-2a²b²)<...
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解
(1)16x^4-72x²+81
=(4x²)²-2×4x×9+9²
=(4x²-9)²
=(2x-3)²(2x+3)²
(2)3(a^4+a²b²+b^4)-9a²b²
=3(a^4+b^4-2a²b²)
=3(a²-b²)²
=3(a+b)²(a-b)²
(3)24a²b²-6(a²+b²)²
=24a²b²-6a^4-12a²b²-6b^4
=-6a^4+12a²b²-6b^4
=-6(a^4-2a²b²+b^4)
=-6(a²-b²)²
=-6(a-b)²(a+b)²
(4)9(x+1)²(x-1)²-6(x²-1)y+y²
=[3(x+1)(x-1)]²-6(x-1)(x+1)y+y²
=[3(x+1)(x-1)-y]²
=(3x²-3-y)²
(5)2(a²+b²)(a+b)²-(a²-b²)²
=2(a²+b²)(a+b)²-(a+b)²(a-b)²
=(a+b)²[2(a²+b²)-(a-b)²]
=(a+b)²(a²+b²+2ab)
=(a+b)^4
收起
16x^4-72x^2y^2+81y^4
=(4x^2-9y^2)^2
=(2x+3y)^2(2x-3y)^2