Question

U'2 (u'2-3u+1)-2u(u'3-3u'2+u)+u'4-3u'3+u'2

Answer 1

2u(2u-3u+1)-2u(3u-3u*2+u)+4u-3u*3+2u=(4u^2-6u^2+2u)-(6u^2-12u^2+2u^2)+4u-9u+2u=4u^2-6u^2+2u-6u^2+12u^2-2u^2-3u= (4u^2-6u^2-6u^2+12u^2-2u^2)+2u-3u= (-2u^2+4u^2)-u=2u^2-u (^2-это значит в квадрате )

Answer 2

To simplify the expression U'2(u'2-3u+1)-2u(u'3-3u'2+u)+U'4-3u'3+u'2, we can expand and combine like terms:

Starting with the first term, U'2(u'2-3u+1), we can distribute U'2 to each term inside the parentheses: U'2 * u'2 - U'2 * 3u + U'2 * 1

This simplifies to: u'4 - 3u'2 + U'2

Moving on to the second term, -2u(u'3-3u'2+u), we can distribute -2u to each term inside the parentheses: -2u * u'3 + 2u * 3u'2 - 2u * u

This simplifies to: -2u'3 + 6u'2 - 2u

Finally, combining all the terms, we have: u'4 - 3u'2 + U'2 - 2u'3 + 6u'2 - 2u + U'4 - 3u'3 + u'2

Combining like terms, we get: u'4 + U'4 - 2u'3 - 3u'3 - 3u'2 + 6u'2 - 2u'2 + u'2 - 2u

Simplifying further, we have: u'4 + U'4 - 5u'3 + 5u'2 - 2u

So the simplified expression is u'4 + U'4 - 5u'3 + 5u'2 - 2u.