请写明过程:因式分解(1)x四次方-10x²+9 (2)x四次方+7x²-18(3)x²-5xy+6y²
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请写明过程:因式分解(1)x四次方-10x²+9 (2)x四次方+7x²-18(3)x²-5xy+6y²
请写明过程:因式分解(1)x四次方-10x²+9 (2)x四次方+7x²-18(3)x²-5xy+6y²
请写明过程:因式分解(1)x四次方-10x²+9 (2)x四次方+7x²-18(3)x²-5xy+6y²
答:都可以用十字相乘法分解
(1)x四次方-10x²+9
=x^4-10x^2+9 (把x^2看成整体,用十字相乘法分解):
=(x^2-1)(x^2-9)
=(x-1)(x+1)(x-3)(x+3)
(2)x四次方+7x²-18
=x^4+7x^2-18
=(x^2+9)(x^2-2)
(3)x²-5xy+6y²
=(x-2y)(x-3y)
(1)x^4-10x^2+9
=(x^2-1)(x^2-9)
=(x+1)(x-1)(x+3)(x-3)
(2)x^4+7x^2-18
=(x^2+9)(x^2-2)
(3)x^2-5xy+6y^2
=(x-3y)(x-2y)
(1)x⁴-10x²+9
=(x²-1)(x²-9)
=(x+1)(x-1)(x+3)(x-3)
(2)x⁴+7x²-18
=(x²+9)(x²-2)
(3)x²-5xy+6y²
=(x-3y)(x-2y)
x^4 - 10x^2 + 9
= (x^2 - 9)(x^2 -1) ------十字相乘
=(x+3)(x-3)(x+1)(x-1) -----------平方差公式
x^4 + 7x^2 -18
= (x^2 + 9)(x^2 -2) -----十字相乘法
=(x^2 + 9)*(x+√2)*(x-√2) --------平方差
x^2 - 5xy +6y^2
=(x - 2y)*(x-3y) ----十字相乘法