Maths identities (urgent)20pts

👨🏻‍🏫 學術台數學

[匿名]

2009-08-01 1:41 am

Plz with solutions:

factorize the following expressions:

1) 32 + 48n + 18n^2

factorize the following expressions:

2) 2a^2 - 28ab + 98b^2

factorize the following expressions:

3) 80r^2 + 40rs + 5s^2

factorize the following expressions:

4) 3x^2 - 18xy + 27y^2

factorize the following expressions:

5) 16(p - 5)^2 + 8(p-5)^2 + 1

factorize the following expressions:

6) (x - y)^2 + 4(x - y) + 4

factorize the following expressions:

7) 9 - 24(h - 5k) + 16(h-5k)^2

factorize the following expressions:

8) 4(x - y)^2 - 4z(x - y) + z^2

factorize the following expressions:

9) w^4 + 2w^2 + 1

factorize the following expressions:

10) x^4 - 6ax^2 + 9a^2

factorize the following expressions:

11) w^3 + 12vw^2 + 36v^2w

factorize the following expressions:

12) 3(3a-b)^2 + 12k(b - 3a) + 12k^2

更新1:

thanks a lot !

回答 (2)

Edward

2009-08-01 1:56 am

✔ 最佳答案

1) 32 + 48n + 18n^2
= 2(9n^2 + 24n + 16)
= 2(3n+4)^2

2) 2a^2 - 28ab + 98b^2
= 2(a^2 - 14ab + 49b^2)
= 2(a-7b)^2

3) 80r^2 + 40rs + 5s^2
= 5(16r^2 + 8rs + s^2)
= 5(4r+s)^2

4) 3x^2 - 18xy + 27y^2
= 3(x^2 - 6xy + 9y^2)
= 3(x-3y)^2

5) 16(p - 5)^2 + 8(p-5)^2 + 1〔直接依照原文〕
= 24(p-5)^2 + 1〔無法再度分解〕

〔推測版本〕
16(p-5)^2 + 8(p-5) + 1
= [4(p-5) + 1]^2 = (4p-5+1)^2
= (4p-4)^2

6) (x - y)^2 + 4(x - y) + 4
= [(x-y) + 2]^2
= (x-y+2)^2

7) 9 - 24(h - 5k) + 16(h-5k)^2
= [3 - 4(h-5k)]^2
=(20k - 4h + 3)^2

8) 4(x - y)^2 - 4z(x - y) + z^2
= [2(x-y) - z]^2
= (2x-2y-z)^2

9) w^4 + 2w^2 + 1
= (w^2 + 1)^2

10) x^4 - 6ax^2 + 9a^2
= (x^2 - 3a)^2

11) w^3 + 12vw^2 + 36v^2w
= w(w^2 + 12vw + 36v^2)
= w(w+6v)^2

12) 3(3a-b)^2 + 12k(b - 3a) + 12k^2
= 3[(3a-b)^2 - 4k(3a-b) + 4k^2]
= 3[(3a-b) - 2k]^2
= 3(3a-b-2k)^2

參考: 自己演算

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用戶7639

2009-08-01 2:03 am

1) 32 + 48n + 18n2
=2(16+24n+9n2)
=2(4+3n)2

2) 2a^2 - 28ab + 98b^2
=2(a2+14ab+49b)
=2(a+7b)2

3) 80r2 + 40rs + 5s2
=5(16r2+8rs+s2)
=5(4r+s)2

4) 3x2 - 18xy + 27y2
=3(x2-6xy+9y2)
=3(x-3y)2

5) 16(p - 5)2 + 8(p-5)2 + 1
=[4(p-5)+1]2
=(4p-20+1)2
=(4p-19)2

6) (x - y)2 + 4(x - y) + 4
=[(x-y)+2]2
=(x-y+2)2

7) 9 - 24(h - 5k) + 16(h-5k)2
=[3-4(h-5k)]2
=(3-4h+20k)2

8) 4(x - y)2 - 4z(x - y) + z2
=[2(x-y)-z]2
=(2x-2y-z)2

9) w4 + 2w2 + 1
=( w2+1)2

10) x4 - 6ax2 + 9a2
=( x2+ 3a)2

11) w3 + 12vw2 + 36v2w
=w(w2+12vw+36v2)
=w(w+4v)2

12) 3(3a-b)2 + 12k(b - 3a) + 12k2
=3(3a-b)2 -12k(3a-b) + 12k2
=3[(3a-b)2 -4k(3a-b) + 4k2]
=3[(3a-b)– 2k]2
=3(3a-b-k)2

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