Factorization

肥胖人

2011-02-06 7:02 am

1. Find out the factors of 4(a+b)^2 - 9(a-b)^2.

2. Factorize x^2 - y^2 + 2x + 1.

3a) Factorize x^2 - 7x -198
3b) Hence, factorize (2y+3)^2 - 7(2y+3) - 198

4a) Factorize 3x^2 - 22x -16
4b) Factorize 27x^3 + 8
4c) Hence, factorize 27x^3 + 9x^2 - 66x -40.

回答 (1)

STEVIE-G™

2011-02-06 7:40 am

✔ 最佳答案

1.
4(a+b)^2-9(a-b)^2
=[2(a+b)]^2-[3(a-b)]^2
=[2(a+b)-3(a-b)][2(a+b)+3(a-b)]
=(5b-a)(5a-b)

2.
x^2-y^2+2x+1
=(x^2+2x+1)-y^2
=(x+1)^2-y^2
=(x+1-y)(x+1+y)

3a)
x^2-7x-198=(x-18)(x+11)

3b)
Let u=2y+3

(2y+3)^2-7(2y+3)-198
=u^2-7u-198
=(u-18)(u+11)
=(2y-15)(2y+14)
=2(y+7)(2y-15)

4a)
3x^2-22x-16=(3x+2)(x-8)

4b)
27x^3+8
=(3x)^3+2^3
=(3x+2)[(3x)^2-(3x)(2)+(2)^2]
=(3x+2)(9x^2-6x+4)

4c)
27x^3+9x^2-66x-40
=(27x^3+8)+(9x^2-66x-48)
=(27x^3+8)+3(3x^2-22x-16)
=(3x+2)(9x^2-6x+4)+3(3x+2)(x-8)
=(3x+2)[(9x^2-6x+4)+3(x-8)]
=(3x+2)(9x^2-3x-20)
=(3x+2)(3x-5)(3x+4)

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