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

Special Case Identification: We are asked to find the square of the binomial (2c - 1). This means we need to calculate (2c - 1)^2. Which special case applies here? (2c - 1)^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 (2c - 1)^2 with (a - b)^2. a = 2c b = 1Application of Formula: Apply the square of a binomial formula to expand (2c - 1)^2. (a - b)^2 = a^2 - 2ab + b^2 (2c - 1)^2 = (2c)^2 - 2(2c)(1) + (1)^2Simplification: Simplify (2c)^2 - 2(2c)(1) + (1)^2. (2c)^2 - 2(2c)(1) + (1)^2 = (2c * 2c) - (2 * 2 * 1)c + 1 * 1 = 4c^2 - 4c + 1

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

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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

(2c - 1)^2

Special Case Identification: We are asked to find the square of the binomial $(2c - 1)$ . This means we need to calculate $(2c - 1)^2$ . Which special case applies here? $(2c - 1)^2$ is in the form of $(a - b)^2$ . Special case: $(a - b)^2 = a^2 - 2ab + b^2$
Values of $a$ and $b$ : Identify the values of $a$ and $b$ . Compare $(2c - 1)^2$ with $(a - b)^2$ . $a = 2c$ $b = 1$
Application of Formula: Apply the square of a binomial formula to expand $(2c - 1)^2$ . $(a - b)^2 = a^2 - 2ab + b^2$ $(2c - 1)^2 = (2c)^2 - 2(2c)(1) + (1)^2$
Simplification: Simplify $(2c)^2 - 2(2c)(1) + (1)^2.$ $(2c)^2 - 2(2c)(1) + (1)^2$ $= (2c \cdot 2c) - (2 \cdot 2 \cdot 1)c + 1 \cdot 1$ $= 4c^2 - 4c + 1$