What is expand (x^3+x^2+1)^2 ?

The solution to expand (x^3+x^2+1)^2 is x^6+2x^5+x^4+2x^3+2x^2+1

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expand (x^3+x^2+1)^2

expand

(x^{3} + x^{2} + 1)^{2}

x^{6} + 2 x^{5} + x^{4} + 2 x^{3} + 2 x^{2} + 1

Solution steps

(x^{3} + x^{2} + 1)^{2}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

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

Distribute parentheses

= x^{3} x^{3} + x^{3} x^{2} + x^{3} \cdot 1 + x^{2} x^{3} + x^{2} x^{2} + x^{2} \cdot 1 + 1 \cdot x^{3} + 1 \cdot x^{2} + 1 \cdot 1

Simplify

x^{3} x^{3} + x^{3} x^{2} + x^{3} \cdot 1 + x^{2} x^{3} + x^{2} x^{2} + x^{2} \cdot 1 + 1 \cdot x^{3} + 1 \cdot x^{2} + 1 \cdot 1 : x^{6} + 2 x^{5} + x^{4} + 2 x^{3} + 2 x^{2} + 1

= x^{6} + 2 x^{5} + x^{4} + 2 x^{3} + 2 x^{2} + 1

(3 a + 4 b)^{3}

\frac{( 2 x ^{3} - 4 x - 2 )}{( 2 x + 2 )}

\frac{4}{3} \cdot 3.14 \cdot 7^{3}

+ 5 - 3

e^{x} \cdot (- e^{x})

What is expand (x^3+x^2+1)^2 ?
The solution to expand (x^3+x^2+1)^2 is x^6+2x^5+x^4+2x^3+2x^2+1