Question

(х+1)(а²-2х+5)+(х²+3)(1-х)=

Answer 1

(х+1)(а²-2х+5)+(х²+3)(1-х)=a²x-2x²+5x+a²-2x+5+x²-x^3+3-3x=a²x-x^3-x²+a²+8.

Ответ: a²x-x^3-x²+a²+8.

Answer 2

Let's simplify the expression step by step:

(х + 1)(а² - 2х + 5) + (х² + 3)(1 - х)

Step 1: Expand both sets of parentheses.

(х * а²) + (х * -2х) + (х * 5) + (1 * а²) + (1 * -2х) + (1 * 5) + (х² * 1) + (х² * -х) + (х² * 3)

Step 2: Simplify each term.

а²х - 2х² + 5х + а² - 2х + 5 + х² - х³ + 3х²

Step 3: Combine like terms.

Group the terms with the same power of x together:

(а²х - 2х) + (х² - х³) + (5х + а² - 2 + 5 + 3х²)

Now, simplify each group:

а²х - 2х + х² - х³ + 8х + а² + 3х² - 2

Step 4: Combine like terms again.

Combine the terms with the same power of x:

х³ + а²х + х² + 8х + а² - 2

So, the simplified expression is:

х³ + а²х + х² + 8х + а² - 2