Question

Преобразуйте в многочлен выражение: (u-4)(u+1) + ( u^2-u+1)(u+1) Пожалуйста

Answer 1

(u-4)(u+1)+(u²-u+1)(u+1)=(u+1)(u-4+u²-u+1)=(u+1)(u²-3)

Answer 2

Converting the Expression to a Polynomial:

To convert the given expression to a polynomial, we can start by multiplying the terms and then simplifying the resulting expression.

The given expression is: (u-4)(u+1) + (u^2-u+1)(u+1)

Let's start by expanding each part of the expression and then simplifying it.

Expanding the first part: (u-4)(u+1) This can be expanded using the distributive property: u(u+1) - 4(u+1)

Expanding the second part: (u^2-u+1)(u+1) This can be expanded using the distributive property: u^2(u+1) - u(u+1) + 1(u+1)

Now, let's simplify each part and then combine them to form the polynomial.

Expanding and simplifying the first part: u(u+1) - 4(u+1) This simplifies to: u^2 + u - 4u - 4

Expanding and simplifying the second part: u^2(u+1) - u(u+1) + 1(u+1) This simplifies to: u^3 + u^2 - u^2 - u + u + 1 Simplified to: u^3 + 1

Now, let's combine the simplified parts: u^2 + u - 4u - 4 + u^3 + 1 This simplifies to: u^3 + u^2 - 3u - 3

So, the given expression (u-4)(u+1) + (u^2-u+1)(u+1), when converted to a polynomial, is equal to u^3 + u^2 - 3u - 3.