How do you expand (x+1)^2(x-3)^2????????

nozar nazari

2009-02-14 9:12 am

✔ 最佳答案

[x^2 -2x -3]^2

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[匿名]

2009-02-14 5:28 pm

here u go
(x+1)^2(x-3)^2
=(x^2+1+2x)(x2+9-6x)
=x^4+9x^2-6x^3+x^2+9-6x+2x^3+18x-12x^2
=x^4-2x^2-4x^3+12x+9 Answer

參考: me

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[匿名]

2009-02-14 5:19 pm

(x + 1)^2(x - 3)^2
= [(x + 1)(x - 3)]^2
= [x*x + 1*x - x*3 - 1*3]^2
= [x^2 + x - 3x - 3]^2
= [x^2 - 2x - 3]^2
= [x^2 - 2x - 3][x^2 - 2x - 3]
= x^2*x^2 - 2x*x^2 - 3*x^2 - x^2*2x + 2x*2x + 3*2x - x^2*3 + 2x*3 + 3*3
= x^4 - 2x^3 - 3x^2 - 2x^3 + 4x^2 + 6x - 3x^2 + 6x + 9
= x^4 - 2x^3 - 2x^3 - 3x^2 + 4x^2 - 3x^2 + 6x + 6x + 9
= x^4 - 4x^3 - 2x^2 + 12x + 9

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[匿名]

2009-02-14 5:14 pm

You do have the first part right, good job.
The second part is harder. Each term in the first polynomial must be multiplied by each term in the second polynomial.

You will come up with nine terms, starting with x^4, and ending with 1*9
After you have all nine terms, group those that have the same exponent:
-6x^3+2x^3=-4x^3
for example.

good luck

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An ESL Learner

2009-02-14 5:13 pm

(x + 1)^2(x - 3)^2
= [(x + 1)(x - 3)]^2
= [x*x + 1*x - x*3 - 1*3]^2
= [x^2 + x - 3x - 3]^2
= [x^2 - 2x - 3]^2
= [x^2 - 2x - 3][x^2 - 2x - 3]
= x^2*x^2 - 2x*x^2 - 3*x^2 - x^2*2x + 2x*2x + 3*2x - x^2*3 + 2x*3 + 3*3
= x^4 - 2x^3 - 3x^2 - 2x^3 + 4x^2 + 6x - 3x^2 + 6x + 9
= x^4 - 2x^3 - 2x^3 - 3x^2 + 4x^2 - 3x^2 + 6x + 6x + 9
= x^4 - 4x^3 - 2x^2 + 12x + 9

Edit: Î£ducator, please don't copy my answer.
Edit(1): Henri C, please don't copy my answer.

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[匿名]

2009-02-14 5:11 pm

(x+1)^2(x-3)^2
(x^2+1)(x^2+9)
=x^4+9x^2+x^2+9
=x^4 - 4x^3 - 2x^2 + 12x + 9

More extensive working:
(x + 1)^2(x - 3)^2
= [(x + 1)(x - 3)]^2
= [x*x + 1*x - x*3 - 1*3]^2
= [x^2 + x - 3x - 3]^2
= [x^2 - 2x - 3]^2
= [x^2 - 2x - 3][x^2 - 2x - 3]
= x^2*x^2 - 2x*x^2 - 3*x^2 - x^2*2x + 2x*2x + 3*2x - x^2*3 + 2x*3 + 3*3
= x^4 - 2x^3 - 3x^2 - 2x^3 + 4x^2 + 6x - 3x^2 + 6x + 9
= x^4 - 2x^3 - 2x^3 - 3x^2 + 4x^2 - 3x^2 + 6x + 6x + 9
= x^4 - 4x^3 - 2x^2 + 12x + 9

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How do you expand (x+1)^2(x-3)^2????????

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