Question

分解因式-2x^4-36x^3-162x^2 2x^2-2x+1/2 -2x^2-12xy-18y2

Answer 1

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数学之美团为你解答

-2x⁴ - 36x³ - 162x²
= - 2x² (x² + 18x + 81)
= - 2x² (x+9)²

2x² - 2x + 1/2
= 1/2 ( 4x² - 4x + 1)
= 1/2 ( 2x - 1)²

- 2x² - 12xy - 18y²
= - 2 (x² + 6xy + 9y²)
= - 2(x+3y)²

考查完全平方公式

Answer 2

-2x^4-36x^3-162x^2
=-2^2(x^2+18x+81)
=-2x^2(x+9)^2

2x^2-2x+1/2
=1/2(4x^2-4x+1)
=1/2(2x-1)^2

-2x^2-12xy-18y^2
=-2x^2-6xy-6xy-18y^2
=-2x^2-6xy-(6xy+18y^2)
=-2x(x+3y)-6y(x+3y)
=(-2x-6y)(x+3y)
=-2(x+3y)^2