What is expand (x^2-x+1)^4 ?

The solution to expand (x^2-x+1)^4 is x^8-4x^7+10x^6-16x^5+19x^4-16x^3+10x^2-4x+1

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expand (x^2-x+1)^4

expand

(x^{2} - x + 1)^{4}

x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 19 x^{4} - 16 x^{3} + 10 x^{2} - 4 x + 1

Solution steps

(x^{2} - x + 1)^{4}

Simplify

(x^{2} - x + 1)^{4} : (x^{2} - x + 1) (x^{2} - x + 1) (x^{2} - x + 1) (x^{2} - x + 1)

= (x^{2} - x + 1) (x^{2} - x + 1) (x^{2} - x + 1) (x^{2} - x + 1)

Expand

(x^{2} - x + 1) (x^{2} - x + 1) : x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1

= (x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1) (x^{2} - x + 1) (x^{2} - x + 1)

Expand

(x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1) (x^{2} - x + 1) : x^{6} - 3 x^{5} + 6 x^{4} - 7 x^{3} + 6 x^{2} - 3 x + 1

= (x^{6} - 3 x^{5} + 6 x^{4} - 7 x^{3} + 6 x^{2} - 3 x + 1) (x^{2} - x + 1)

Distribute parentheses

= x^{6} x^{2} + x^{6} (- x) + x^{6} \cdot 1 - 3 x^{5} x^{2} - 3 x^{5} (- x) - 3 x^{5} \cdot 1 + 6 x^{4} x^{2} + 6 x^{4} (- x) + 6 x^{4} \cdot 1 - 7 x^{3} x^{2} - 7 x^{3} (- x) - 7 x^{3} \cdot 1 + 6 x^{2} x^{2} + 6 x^{2} (- x) + 6 x^{2} \cdot 1 - 3 x x^{2} - 3 x (- x) - 3 x \cdot 1 + 1 \cdot x^{2} + 1 \cdot (- x) + 1 \cdot 1

Simplify

x^{6} x^{2} + x^{6} (- x) + x^{6} \cdot 1 - 3 x^{5} x^{2} - 3 x^{5} (- x) - 3 x^{5} \cdot 1 + 6 x^{4} x^{2} + 6 x^{4} (- x) + 6 x^{4} \cdot 1 - 7 x^{3} x^{2} - 7 x^{3} (- x) - 7 x^{3} \cdot 1 + 6 x^{2} x^{2} + 6 x^{2} (- x) + 6 x^{2} \cdot 1 - 3 x x^{2} - 3 x (- x) - 3 x \cdot 1 + 1 \cdot x^{2} + 1 \cdot (- x) + 1 \cdot 1 : x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 19 x^{4} - 16 x^{3} + 10 x^{2} - 4 x + 1

= x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 19 x^{4} - 16 x^{3} + 10 x^{2} - 4 x + 1

12 x - x

12 x + 2

\frac{44}{66}

- 4 i \times 5 i

\frac{4 6}{2} 3

What is expand (x^2-x+1)^4 ?
The solution to expand (x^2-x+1)^4 is x^8-4x^7+10x^6-16x^5+19x^4-16x^3+10x^2-4x+1