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quad(5+2sqrt3)^(2)

$1$ ) $\quad(5+2 \sqrt{3})^{2}$

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Add and subtract polynomials

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Q.

1

)

\quad(5+2 \sqrt{3})^{2}

Identify Expression: Identify the expression to be squared. $\newline$ We need to square the expression $(5 + 2\sqrt{3})$ . This means we will multiply the expression by itself.
Apply Formula: Apply the formula for the square of a binomial. $\newline$ The square of a binomial $(a + b)^2$ is given by $a^2 + 2ab + b^2$ . Here, $a$ is $5$ and $b$ is $2\sqrt{3}$ .
Square First Term: Square the first term. $\newline$ Square the first term $5$ to get $5^2$ , which is $25$ .
Multiply and Double: Multiply the terms together and double them. Multiply $5$ by $2\sqrt{3}$ to get $10\sqrt{3}$ , and then double this product to account for the $2ab$ term, resulting in $2 \times 10\sqrt{3} = 20\sqrt{3}$ .
Square Second Term: Square the second term. $\newline$ Square the second term $2\sqrt{3}$ to get $(2\sqrt{3})^2$ . Since $(\sqrt{3})^2$ is $3$ , we have $(2^2) \times 3 = 4 \times 3 = 12$ .
Combine Terms: Combine all the terms. $\newline$ Add the results from steps $3$ , $4$ , and $5$ to get the final answer: $25 + 20\sqrt{3} + 12$ .
Simplify Expression: Simplify the expression. $\newline$ Combine the like terms (the constants $25$ and $12$ ) to get $25 + 12 + 20\sqrt{3}$ , which simplifies to $37 + 20\sqrt{3}$ .

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