Задание 318

Решение:

• \({\largeа)}\ (x^2+y^2+x+y)(x+y+xy)=x^3\ +\) \(xy^2\) \(+\ x^2\ +\) \(xy\) \(+\) \(x^2y\) \(+\ y^3\ +\) \(xy\) \(+\ y^2+x^3y+xy^3\ +\) \(x^2y\) \(+\) \(xy^2\) \(=x^3+x^3y+x^2+2x^2y+xy^3+2xy^2+2xy+y^3+y^2\)

• \({\largeб)}\ (2a^2bc-3b^2c-7bc^2)(a^2c-b^3c^2+3bc^3-8c^2)=2a^4bc^2-3a^2b^2c^2\ -\) \(7a^2bc^3\) \(-\ 2a^2b^4c^3+3b^5c^3+7b^4c^4+6a^2b^2c^4-9b^3c^4-21b^2c^5\ -\) \(16a^2bc^3\) \(+\ 24b^2c^3+56bc^4=2a^4bc^2-3a^2b^2c^2-23a^2bc^3-2a^2b^4c^3+3b^5c^3+7b^4c^4+6a^2b^2c^4-9b^3c^4-21b^2c^5+24b^2c^3+56bc^4\)

• \({\largeв)}\ (m^2-mn^2-mn-n^2)(m-mn-n^2+n)=m^3\ -\) \(m^2n^2\) \(-\) \(m^2n\) \(-\) \(mn^2\) \(-\ m^3n+m^2n^3\ +\) \(m^2n^2\) \(+\) \(mn^3\) \(-\) \(m^2n^2\) \(+\ mn^4\ +\) \(mn^3\) \(+\ n^4\ +\) \(m^2n\) \(-\) \(mn^3\) \(-\) \(mn^2\) \(-\ n^3=m^3-m^3n+m^2n^3-m^2n^2+mn^4+mn^3-2mn^2+n^4-n^3\)

• \({\largeг)}\ (0{,}1p^3-2p^2q-0{,}5pq^2+1{,}2p^3)(8p^2-0{,}2pq+5q^2)=(1{,}3p^3-2p^2q-0{,}5pq^2)(8p^2-0{,}2pq+5q^2)=10{,}4p^5\ -\) \(16p^4q\) \(-\) \(4p^3q^2\) \(-\) \(0{,}26p^4q\) \(+\) \(0{,}4p^3q^2\) \(+\) \(0{,}1p^2q^3\) \(+\) \(6{,}5p^3q^2\) \(-\) \(10p^2q^3\) \(-\ 2{,}5pq^4=10{,}4p^5-16{,}26p^4q+2{,}9p^3q^2-9{,}9p^2q^3-2{,}5pq^4\)