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

Identify Special Case: We are asked to find the square of the binomial (4c + 1). This means we need to calculate (4c + 1)^2. Which special case applies here? (4c + 1)^2 is in the form of (a + b)^2. Special case: (a + b)^2 = a^2 + 2ab + b^2Determine a and b: Identify the values of a and b. Compare (4c + 1)^2 with (a + b)^2. a = 4c b = 1Apply Binomial Formula: Apply the square of a binomial formula to expand (4c + 1)^2. (a + b)^2 = a^2 + 2ab + b^2 (4c + 1)^2 = (4c)^2 + 2(4c)(1) + 1^2Simplify Expression: Simplify (4c)^2 + 2(4c)(1) + 1^2. (4c)^2 + 2(4c)(1) + 1^2 = (4c * 4c) + (2 * 4 * 1)c + 1 * 1 = 16c^2 + 8c + 1

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Find the square. Simplify your answer. $\newline$ $(4c + 1)^2$

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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

(4c + 1)^2

Identify Special Case: We are asked to find the square of the binomial $(4c + 1)$ . This means we need to calculate $(4c + 1)^2$ . $\newline$ Which special case applies here? $\newline$ $(4c + 1)^2$ is in the form of $(a + b)^2$ . $\newline$ Special case: $(a + b)^2 = a^2 + 2ab + b^2$
Determine $a$ and $b$ : Identify the values of $a$ and $b$ . Compare $(4c + 1)^2$ with $(a + b)^2$ . $a = 4c$ $b = 1$
Apply Binomial Formula: Apply the square of a binomial formula to expand $(4c + 1)^2$ . $\newline$ $(a + b)^2 = a^2 + 2ab + b^2$ $\newline$ $(4c + 1)^2 = (4c)^2 + 2(4c)(1) + 1^2$
Simplify Expression: Simplify $(4c)^2 + 2(4c)(1) + 1^2.$ $(4c)^2 + 2(4c)(1) + 1^2$ $= (4c \times 4c) + (2 \times 4 \times 1)c + 1 \times 1$ $= 16c^2 + 8c + 1$