Question

Multiply
x² + x + 1 by x² - x + 1 ​​

Answer 1

Given Expression :

• (x² + x + 1) × (x² - x + 1)

To find :

• Product of (x² + x + 1) and (x² - x + 1).

Clarification :

Here, we have to multiply a polynomial with more than two terms. In order to multiply a polynomial with more than two terms, we multiply all the terms of the second polynomial by each term of the first polynomial. At the the expression we'll get will be our answer.

☀ So, let's commence the steps..!

Explication of steps :

➝ (x² + x + 1) × (x² - x + 1)

➝ x²(x² - x + 1) + x(x² - x + 1) + 1(x² - x + 1)

➝ x²(x²) + x²(- x) + x²(1) + x(x²) + x(- x) + x(1) + 1(x²) + 1(- x) + 1(1)

➝ x⁴ - x³ + x² + x³ - x² + x + x² - x + 1

➝ x⁴ - x³ + x³ + x² - x² + x² + x - x + 1

➝ x⁴ + x² + 1

Therefore, x⁴ + x² + 1 is the required answer.