Find the square. Simplify your answer. (4n + 3)^2 ______

Special Case Identification: We are asked to find the square of the binomial (4n + 3). This means we need to calculate (4n + 3)^2. Which special case applies here? (4n + 3)^2 is in the form of (a + b)^2. Special case: (a + b)^2 = a^2 + 2ab + b^2Values of a and b: Identify the values of a and b. Compare (4n + 3)^2 with (a + b)^2. a = 4n b = 3Application of Binomial Formula: Apply the square of a binomial formula to expand (4n + 3)^2. (a + b)^2 = a^2 + 2ab + b^2 (4n + 3)^2 = (4n)^2 + 2(4n)(3) + 3^2Simplification: Simplify (4n)^2 + 2(4n)(3) + 3^2. (4n)^2 + 2(4n)(3) + 3^2 = (4n * 4n) + (2 * 4 * 3)n + 3 * 3 = 16n^2 + 24n + 9

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Find the square. Simplify your answer. $\newline$ $(4n + 3)^2$

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Math Problems

Algebra 1

Multiply two binomials: special cases

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Q. Find the square. Simplify your answer.

\newline

(4n + 3)^2

Special Case Identification: We are asked to find the square of the binomial $(4n + 3)$ . This means we need to calculate $(4n + 3)^2$ . $\newline$ Which special case applies here? $\newline$ $(4n + 3)^2$ is in the form of $(a + b)^2$ . $\newline$ Special case: $(a + b)^2 = a^2 + 2ab + b^2$
Values of $a$ and $b$ : Identify the values of $a$ and $b$ . $\newline$ Compare $(4n + 3)^2$ with $(a + b)^2$ . $\newline$ a = $4n$ $\newline$ b = $3$
Application of Binomial Formula: Apply the square of a binomial formula to expand $(4n + 3)^2$ . $(a + b)^2 = a^2 + 2ab + b^2$ $(4n + 3)^2 = (4n)^2 + 2(4n)(3) + 3^2$
Simplification: Simplify $(4n)^2 + 2(4n)(3) + 3^2.$ $(4n)^2 + 2(4n)(3) + 3^2$ $= (4n \times 4n) + (2 \times 4 \times 3)n + 3 \times 3$ $= 16n^2 + 24n + 9$