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

The solution to expand (3x^2+2x+1)^2 is 9x^4+12x^3+10x^2+4x+1

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

expand

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

9 x^{4} + 12 x^{3} + 10 x^{2} + 4 x + 1

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

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

Simplify

3 x^{2} \cdot 3 x^{2} + 3 x^{2} \cdot 2 x + 3 x^{2} \cdot 1 + 2 x \cdot 3 x^{2} + 2 x \cdot 2 x + 2 x \cdot 1 + 1 \cdot 3 x^{2} + 1 \cdot 2 x + 1 \cdot 1 : 9 x^{4} + 12 x^{3} + 10 x^{2} + 4 x + 1

= 9 x^{4} + 12 x^{3} + 10 x^{2} + 4 x + 1

27 x^{3} y^{3} - 1

6 \frac{3}{2}

\frac{2 + 3 i}{4 - 5 i}

- 24 a^{x + 2} - 15 a^{x + 2} + 39 a^{x + 2}

27 m^{3} + 125 n^{3}

What is expand (3x^2+2x+1)^2 ?
The solution to expand (3x^2+2x+1)^2 is 9x^4+12x^3+10x^2+4x+1