Question

(x+1)(x^2-x+1)(x^6-x^3+1)=

Answer 1

Ответ: $x^{9} +1$

Решаем, используя формулы сокращённого умножения:

Answer 2

To expand the expression $(x+1)(x^2-x+1)(x^6-x^3+1)$, you can use the distributive property to multiply each term in the first factor by each term in the second factor, and then multiply the result by the third factor. Here's the step-by-step expansion:

1. Multiply the first two factors: $(x+1)(x^2-x+1) = x(x^2-x+1) + 1(x^2-x+1)$ Distribute the terms: $x(x^2-x+1) = x^3 - x^2 + x$ $1(x^2-x+1) = x^2 - x + 1$

2. Now, multiply the result from step 1 by the third factor: $(x^3 - x^2 + x)(x^6-x^3+1)$

3. Distribute the terms: $x^3(x^6-x^3+1) - x^2(x^6-x^3+1) + x(x^6-x^3+1)$

4. Multiply each term in the expression by the corresponding term in the third factor: $x^9 - x^6 + x^3 - x^8 + x^5 - x^2 + x^7 - x^4 + x - x^4 + x^2 - x$

5. Combine like terms: $x^9 - x^8 + x^7 - x^6 + x^5 - x^4 + x^3 - x$

So, the expanded expression is: $x^9 - x^8 + x^7 - x^6 + x^5 - x^4 + x^3 - x$

This is the final expanded form of the expression $(x+1)(x^2-x+1)(x^6-x^3+1)$.