急!!!数学 Trinomial

YipWing yan

2012-12-11 10:45 pm

Factor the following trinomial.

please show all the steps clearly.

1) 12x^4-25x^2y^2-7y^4

Thank you.

回答 (2)

用戶2053

2012-12-11 11:54 pm

✔ 最佳答案

Method 1 : 12x⁴- 25x²y² - 7y⁴
= 12x⁴+ 3x²y² - 28x²y² - 7y⁴
= 3x² (4x² + y²) - 7y²(4x² + y²)
= (4x² + y²) (3x² - 7y²) Method 2 : 12x⁴- 25x²y² - 7y⁴
= y⁴[12(x/y)⁴- 25(x/y)² - 7]
Let k = x²/y² :
= y⁴(12k² - 25k - 7)
= y⁴(4k + 1)(3k - 7)
= y⁴(4x²/y² + 1)(3x²/y² - 7)
= y² (4x²/y² + 1) y² (3x²/y² - 7)
= (4x² + y²) (3x² - 7y²) Method 3 : 4x².........y²
.......X
3x².....- 7y²
────────────────
- 28x²y² + 3x²y² = - 25x²y²∴
12x⁴- 25x²y² - 7y⁴
= (4x² + y²) (3x² - 7y²)

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用戶10012

2012-12-12 3:04 am

Let x^2 = u and y^2 = v, so the expression changed to
12u^2 - 25uv - 7v^2
= (4u + v)(3u - 7v)
= (4x^2 + y^2)(3x^2 - 7y^2)

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