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

Algebra 1

Add and subtract polynomials

Full solution

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\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 $37 + 20\sqrt{3}$ .