Задание 296

Решение:

• $${\largeа)}\ (a+1)(a+1)(a+1)=(a^2+a+a+1)(a+1)=(a^2+2a+1)(a+1)=a^3+2a^2+a+a^2+2a+1=a^3+3a^2+3a+1$$

• $${\largeб)}\ (x-1)(x-1)(x-1)=(x^2-x-x+1)(x-1)=(x^2-2x+1)(x-1)=x^3-2x^2+x-x^2+2x-1=x^3-3x^2+3x-1$$

• $${\largeв)}\ (a+b)(a-b)(a+b)=(a^2+ab-ab-b^2)(a+b)=(a^2-b^2)(a+b)=a^3-ab^2+a^2b-b^3$$

• $${\largeг)}\ (m-n)(m-n)(m+n)=(m^2-mn-mn+n^2)(m+n)=(m^2-2mn+n^2)(m+n)=m^3-2m^2n+mn^2+m^2n-2mn^2+n^3=m^3-m^2n-mn^2+n^3$$

• $${\largeд)}\ (a+b+c)(a+1)=a^2+ab+ac+a+b+c$$

• $${\largeе)}\ (a-b-c)(a-1)=a^2-ab-ac-a+b+c$$

• $${\largeж)}\ (x+1)(x^2-x+1)=x^3-x^2+x+x^2-x+1=x^3+1$$

• $${\largeз)}\ (x-1)(x^2+x+1)=x^3+x^2+x-x^2-x-1=x^3-1$$

• $${\largeи)}\ (x^3+2x-3)(2-3x)=2x^3+4x-6-3x^4-6x^2+9x=2x^3+13x-6-3x^4-6x^2$$

• $${\largeк)}\ (5m^2-3mn+n^2)(2n-m^2)=10m^2n-6mn^2+2n^3-5m^4+3m^3n-m^2n^2$$

• $${\largeл)}\ (a+b+c)(a+b-c)=a^2+ab+ac+ab+b^2+bc-ac-bc-c^2=a^2+2ab+b^2-c^2$$

• $${\largeм)}\ (a-b+c)(a-b-c)=a^2-ab+ac-ab+b^2-bc-ac+bc-c^2=a^2-2ab+b^2-c^2$$