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

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

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

expand

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

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

Simplify

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

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

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

(3 x + 2)^{2}

12 - 3 x

\frac{1}{8 x} + \frac{3}{8 x ^{2}}

\frac{- 3}{12}

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