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July 2022
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Преобразуйте выражение в многочлен стандартного вида
а) 2(а-1)²+3(а-2)²=
б) 4 (m-2n)²-3(3m+n)²=
в) 2(p-3q)²-4(2p-q)²-(2q-3p)(p+q)=
г) 4(3ч+4у)
²-7(2х-3у)²=
Напишите решение и ответ конечно. Заранее спасибо.
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Answers & Comments
Yena
А) 2(а-1)²+3(а-2)²=2(a²-2a+1)+3(a²-4a+4)=2a²-4a+2+3a²-12a+12=5a²-16a+14
б) 4 (m-2n)²-3(3m+n)²=4(m
²-4mn+4n²)-3(9m²+6mn+n²)=
=4m²-16mn+16n²-27m²-18mn-3n²=-23m²-34mn+13n²
в) 2(p-3q)²-4(2p-q)²-(2q-3p)(p+q)=2(p²-6pq+9q²)-4(4p²-4pq+q²)-(2pq+2q²-3p²-3pq
)=
=
2p²-12pq+18q²-16p²+16pq-4q²-2pq-2q²+3p²+3pq=-11p²+5pq+12q²
г) 4(3x+4y)²-7(2x-3y)²=4(9x²+24xy+16y²)-7(2x²-12xy+9y²)=
=36x²+96xy+64y²-14x²+84xy-63y²=22x²+180xy+y²
3 votes
Thanks 2
Chewrolet
Спасибо огромное! Ты мне жизнь спасла!
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Answers & Comments
б) 4 (m-2n)²-3(3m+n)²=4(m²-4mn+4n²)-3(9m²+6mn+n²)=
=4m²-16mn+16n²-27m²-18mn-3n²=-23m²-34mn+13n²
в) 2(p-3q)²-4(2p-q)²-(2q-3p)(p+q)=2(p²-6pq+9q²)-4(4p²-4pq+q²)-(2pq+2q²-3p²-3pq)=
=2p²-12pq+18q²-16p²+16pq-4q²-2pq-2q²+3p²+3pq=-11p²+5pq+12q²
г) 4(3x+4y)²-7(2x-3y)²=4(9x²+24xy+16y²)-7(2x²-12xy+9y²)=
=36x²+96xy+64y²-14x²+84xy-63y²=22x²+180xy+y²