What is (1+xsqrt(3))^2 ?

The solution to (1+xsqrt(3))^2 is 1+2sqrt(3)x+3x^2

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simplify (1+xsqrt(3))^2

simplify

(1 + x 3)^{2}

1 + 23 x + 3 x^{2}

Solution steps

(1 + x 3)^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

1^{2} = 1

2 \cdot 1 \cdot x 3 = 23 x

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

= 1 + 23 x + 3 x^{2}

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