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

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

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simplify (1+xsqrt(2))^2

simplify

(1 + x 2)^{2}

1 + 22 x + 2 x^{2}

Solution steps

(1 + x 2)^{2}

Apply Perfect Square Formula:

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

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

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

1^{2} = 1

2 \cdot 1 \cdot x 2 = 22 x

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

= 1 + 22 x + 2 x^{2}

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