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

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

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

expand

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

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

Simplify

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

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

\frac{e ^{- x} - e ^{- x} x}{e ^{x}}

7 (16)

5 (x + 1) (x + 2)

5 x^{2} + 11 x - 36

12 e^{0.8}

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