Anastasiya scrive: Scomposizione polinomi

Oggetto: Scomposizione polinomi

Corpo del messaggio:
1. (ab-1)^2 – 1

$(ab-1)^2-1=(ab-1+1)(ab-1-1)=ab(ab-2)$

2. 25(a-b)^2 – 16(a+b) ^2

$25(a-b)^2-16(a+b)^2=(5(a-b)+4(a+b))(5(a-b)-4(a+b))=$

$=(5a-5b+4a+4b)(5a-5b-4a-4b)=(9a-b)(a-9b)$

3.(a+3b)^2 – 25b^2

$(a+3b)^2-25b^2=(a+3b+5b)(a+3b-5b)=(a+8b)(a-2b)$

4. (2a^2 – 3)^2 – 8

$(2a^2-3)^2-8=(2a^2-3+2\sqrt 2)(2a^2-3-2\sqrt 2)$

5. 5b^2 (b-3)-b^2 +9

$5b^2(b-3)-b^2+9=5b^2(b-3)-(b-3)(b+3)=(b-3)(5b^2-b-3)$

6.(m^2 + 2)^2 – 12(m^2+2)+36

$(m^2+2)^2-12(m^2+2)+36=(m^2+2-6)^2=(m^2-4)^2$

7.(a-2b)^3 +(a+b) ^3

$(a-2b)^3+(a+b)^3=(a-2b+a+b)((a-2b)^2-(a-2b)(a+b)+(a+b)^2)=$

$=(2a-b)(a^2-4ab+4b^2-a^2-ab+2ab+2b^2+a^2+2ab+b^2)=$

$=(2a-b)(a^2-ab+7b^2)$
8. 125b^3 – (b-3)^3

$125b^3-(b-3)^3=(5b-(b-3))(25b^2+5b(b-3)+(b-3)^2)=$

$=(5b-b+3)(25b^2+5b^2-15b+b^2-6b+9)=(4b+3)(31b^2-21b+9)$
9. 27y^3-(x-4y)^3

$27y^3-(x-4y)^3=(3y-(x-4y))(9y^2+3y(x-4y)+(x-4y)^2)=$

$=(7y-x)(9y^2+3xy-12y^2+x^2-8xy+16y^2)=(7y-x)(x^2-5xy+13y^2)$

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