標題:

F.3 factorization (20分)

發問:

請factorize: 1. 64(m^2)(n^2)-(m+n)^2 2. 75(m^2)-30mn+3(n^2) 3. 4(a^2)+4ab+(b^2)-64 4. 4(x^2)-36(z^2)-28xy+49(y^2) 5. (3a+2b)^2 - 18(3a+2b)+81 6. (4x+5)[4(x^2)+1]-4x-5 7. 8(c+2d)^2-50(3c-d)^2 8. (x-2y)^2-(9a^2)-54ay-81y^2 Thanks!!!

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最佳解答:

1. 64(m^2)(n^2)-(m+n)^2 =(8mn)^2-(m+n)^2 =(8mn+m+n)(8mn-m-n) 2. 75(m^2)-30mn+3(n^2) =3(25m^2-10mn+n^2) =3[(5m)^2-2(5m)(n)+(n)^2] =3(5m-n)^2 3. 4(a^2)+4ab+(b^2)-64 =(2a)^2+2(2a)(b)+b^2-8^2 =(2a+b)^2-8^2 =(2a+b-8)(2a+b+8) 4. 4(x^2)-36(z^2)-28xy+49(y^2) =4x^2-28xy+49y^2-36z^2 =(2x)^2-(2)(2x)(7y)+(7y)^2-(6z)^2 =(2x-7y)^2-(6z)^2 =(2x-7y+6z)(2x-7y-6z) 5. (3a+2b)^2 - 18(3a+2b)+81 =(3a+2b)^2-2(9)(3a+2b)+9^2 =(3a+2b-9)^2 6. (4x+5)[4(x^2)+1]-4x-5 =(4x+5)(4x^2+1)-(4x+5) =(4x+5)(4x^2+1-1) =(4x+5)(4x^2) 7. 8(c+2d)^2-50(3c-d)^2 =2[4(c+2d)^2-25(3c-d)^2] =2{[2(c+2d)]^2-[5(3c-d)]^2]} =2[2(c+2d)+5(3c-d)][2(c+2d)-5(3c-d)] =2[2c+4d+15c-5d][2c+4d-15c+5d] =2(17c-d)(-13c+9d) 8. (x-2y)^2-(9a^2)-54ay-81y^2 =(x-2y)^2-9(a^2+6ay+9y^2) =(x-2y)^2-9(a+3y)^2 =(x-2y)^2-[3(a+3y)]^2 =(x-2y+3a+9y)(x-2y-3a-9y) =(x+3a+3y)(x-3a-11y)

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