udd18ql48m的部落格

標題:

Factorize each of the following expressions (10點!!)

發問:

• Math--Applications in Trigonom@1@
• 法國自由行
• 陳奕迅-我的快樂時代cd 邊一個版本有側紙-@1@

 

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1) (a+b)^2 - 10(a+b) + 252) x^2 - 2uv + y^2 - u^2 - 2xy - v^23) x^2 + 2x + 1 - y^2 4) 4 - x^2 + 2xy - y^25) 4(x-y)^2 - 25(2x+y)^26) (2x-3)^2 + 2(2x-3)y + y^2 7) x^2 - y^2 + 2yz - z^28) 9x^4 - y^2 - 9z^2 + 6yz9) x^2 - y^2 - 25 + 10y + 4z^210) x^2 - y^2 +2yz -z^2 P.S. 例如:(a+b)^2 中的^2等於(a+b)的2次方please... 顯示更多 1) (a+b)^2 - 10(a+b) + 25 2) x^2 - 2uv + y^2 - u^2 - 2xy - v^2 3) x^2 + 2x + 1 - y^2 4) 4 - x^2 + 2xy - y^2 5) 4(x-y)^2 - 25(2x+y)^2 6) (2x-3)^2 + 2(2x-3)y + y^2 7) x^2 - y^2 + 2yz - z^2 8) 9x^4 - y^2 - 9z^2 + 6yz 9) x^2 - y^2 - 25 + 10y + 4z^2 10) x^2 - y^2 +2yz -z^2 P.S. 例如:(a+b)^2 中的^2等於(a+b)的2次方 please show the STEPS clearly on each questions. 請盡快答我,好急的!! {{無言感謝~

最佳解答:

1)(a+b)2 - 10(a+b) + 25 =[(a+b) + 5]2 = (a+b+5)2 2) x2 - 2uv + y2 - u2 - 2xy - v2 = (x2 - 2xy + y2) – (u2 + 2 uv + v2) = (x – y)2 - (u + v)2 = (x – y – u – v)(x – y + u + v) 3) x2 + 2x + 1 - y2 = (x+1)2 – y2 = (x + 1 + y)(x + 1 – y) 4) 4 - x2 + 2xy - y2 = 22 – (x- y)2 = (2 – x + y)(2 + x – y) 5) 4(x-y)2 - 25(2x+y)2 = [2(x-y) – 5(2x + y)][2(x-y) + 5(2x + y)] = [2x-2y – 10x - 5y)][2x-2y + 10x + 5y] = -(8x + 7y)(12x + 3y) = -3(8x + 7y)(4x + y) 6) (2x-3)2 + 2(2x-3)y + y2 = (2x – 3 + y)2 7) x2 - y2 + 2yz - z2 = x2 – (y – z)2 = (x – y + z)(z + y – z) 8) 9x4 - y2 - 9z2 + 6yz = (3x2)2 – (y – 3z)2 = (3x2 – y + 3z)(3x2 + y – 3z) 9) x2 - y2 - 25 + 10y + 4z2 = x2 + 4z2 – (y – 5)2 (無得分解) 10) x2 - y2 +2yz -z2 = x2 – (y – z)2 = (x – y + z)(z + y – z)

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