What is expand (r^2+1+2sqrt(33))^2 ?

The solution to expand (r^2+1+2sqrt(33))^2 is r^4+2r^2(1+2sqrt(33))+4sqrt(33)+133

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expand (r^2+1+2sqrt(33))^2

expand

(r^{2} + 1 + 233)^{2}

r^{4} + 2 r^{2} (1 + 233) + 433 + 133

Solution steps

(r^{2} + 1 + 233)^{2}

Apply exponent rule:

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

(r^{2} + 1 + 233)^{2} = (r^{2} + 1 + 233) (r^{2} + 1 + 233)

= (r^{2} + 1 + 233) (r^{2} + 1 + 233)

Distribute parentheses

= r^{2} r^{2} + r^{2} \cdot 1 + r^{2} \cdot 233 + 1 \cdot r^{2} + 1 \cdot 1 + 1 \cdot 233 + 233 r^{2} + 233 \cdot 1 + 233 \cdot 233

Simplify

r^{2} r^{2} + r^{2} \cdot 1 + r^{2} \cdot 233 + 1 \cdot r^{2} + 1 \cdot 1 + 1 \cdot 233 + 233 r^{2} + 233 \cdot 1 + 233 \cdot 233 : r^{4} + 2 r^{2} (1 + 233) + 433 + 133

= r^{4} + 2 r^{2} (1 + 233) + 433 + 133

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What is expand (r^2+1+2sqrt(33))^2 ?
The solution to expand (r^2+1+2sqrt(33))^2 is r^4+2r^2(1+2sqrt(33))+4sqrt(33)+133