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

The solution to expand (x^2+3x+1)^2 is x^4+6x^3+11x^2+6x+1

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

expand

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

x^{4} + 6 x^{3} + 11 x^{2} + 6 x + 1

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

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

Simplify

x^{2} x^{2} + x^{2} \cdot 3 x + x^{2} \cdot 1 + 3 x x^{2} + 3 x \cdot 3 x + 3 x \cdot 1 + 1 \cdot x^{2} + 1 \cdot 3 x + 1 \cdot 1 : x^{4} + 6 x^{3} + 11 x^{2} + 6 x + 1

= x^{4} + 6 x^{3} + 11 x^{2} + 6 x + 1

(12 x^{- 4} y^{8})^{3}

5 - 2 (4 + - 10)

(64 a^{16})^{\frac{1}{4}}

\frac{5 + 4 i}{2 i}

\frac{5}{3} - \frac{7}{6}

What is expand (x^2+3x+1)^2 ?
The solution to expand (x^2+3x+1)^2 is x^4+6x^3+11x^2+6x+1