Find the square. Simplify your answer. (4g + 1)^2 ______

Identify binomial and formula: Identify the binomial to be squared and the special case formula to use. The given binomial is (4g + 1), and we need to square it. The special case formula for the square of a binomial (a + b)^2 is a^2 + 2ab + b^2.Identify values of a and b: Identify the values of a and b in the binomial. In the binomial (4g + 1), a is 4g and b is 1.Apply binomial formula: Apply the square of a binomial formula to expand (4g + 1)^2. Using the formula (a + b)^2 = a^2 + 2ab + b^2, we get: (4g + 1)^2 = (4g)^2 + 2*(4g)*1 + 1^2Simplify each term: Simplify each term in the expansion. (4g)^2 = 16g^2 (since 4g * 4g = 16g^2) 2*(4g)*1 = 8g (since 2 * 4g * 1 = 8g) 1^2 = 1 (since 1 * 1 = 1) So, (4g + 1)^2 = 16g^2 + 8g + 1

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Algebra 1

Multiply two binomials: special cases

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Q. Find the square. Simplify your answer.

\newline

(4g + 1)^2

Identify binomial and formula: Identify the binomial to be squared and the special case formula to use. $\newline$ The given binomial is $(4g + 1)$ , and we need to square it. The special case formula for the square of a binomial $(a + b)^2$ is $a^2 + 2ab + b^2$ .
Identify values of a and b: Identify the values of $a$ and $b$ in the binomial. In the binomial $(4g + 1)$ , $a$ is $4g$ and $b$ is $1$ .
Apply binomial formula: Apply the square of a binomial formula to expand $(4g + 1)^2$ . Using the formula $(a + b)^2 = a^2 + 2ab + b^2$ , we get: $(4g + 1)^2 = (4g)^2 + 2\cdot(4g)\cdot1 + 1^2$
Simplify each term: Simplify each term in the expansion. $\newline$ $(4g)^2 = 16g^2$ (since $4g \times 4g = 16g^2$ ) $\newline$ $2\times(4g)\times1 = 8g$ (since $2 \times 4g \times 1 = 8g$ ) $\newline$ $1^2 = 1$ (since $1 \times 1 = 1$ ) $\newline$ So, $(4g + 1)^2 = 16g^2 + 8g + 1$