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klim321
@klim321
September 2021
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Примеры 2.6-2.10 пожалуйста
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Гоша68
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2.6 x^3-(y-1)^3=(x-y+1)(x^2+x(y-1)+(y-1)^2)
(2x)^2+(y+2)^3=(2x+y+2)(4x^2+(y+2)^2-2x(y+2))
2.7 (a-b)(a+b)((a-b)^2-(a+b)^2)=(a^2-b^2)(a-b-a-b)(a-b+a+b)=2a*2b(b^2-a^2)=4ab(b^2-a^2)
(a-b)^2(a+b)^2((a+b)^3+(a-b)^3))=(a^2-b^2)^2*2a*(a^2+b^2+a^2+b^2-a^2+b^2)=
=(a^2-b^2)^2*2a*(3b^2+a^2)
2.8 (n^2-6)^2-20
(m^2+1)^2+8
(p^2+18)^2-36p^2=(p^2+18-6p)(p^2+18+6p)
2.9 (x^4-1)-x(x^2-1)=(x^2+1)(x^2-x-1)
y^8-16-y^2(y^4+4)=(y^4+4)(y^4-4-y^2)
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Answers & Comments
Verified answer
2.6 x^3-(y-1)^3=(x-y+1)(x^2+x(y-1)+(y-1)^2)(2x)^2+(y+2)^3=(2x+y+2)(4x^2+(y+2)^2-2x(y+2))
2.7 (a-b)(a+b)((a-b)^2-(a+b)^2)=(a^2-b^2)(a-b-a-b)(a-b+a+b)=2a*2b(b^2-a^2)=4ab(b^2-a^2)
(a-b)^2(a+b)^2((a+b)^3+(a-b)^3))=(a^2-b^2)^2*2a*(a^2+b^2+a^2+b^2-a^2+b^2)=
=(a^2-b^2)^2*2a*(3b^2+a^2)
2.8 (n^2-6)^2-20
(m^2+1)^2+8
(p^2+18)^2-36p^2=(p^2+18-6p)(p^2+18+6p)
2.9 (x^4-1)-x(x^2-1)=(x^2+1)(x^2-x-1)
y^8-16-y^2(y^4+4)=(y^4+4)(y^4-4-y^2)