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

Special Case Identification: We are asked to find the square of the binomial (3c + 3). This means we need to calculate (3c + 3)^2. Which special case applies here? (3c + 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 (3c + 3)^2 with (a + b)^2. a = 3c b = 3Application of Binomial Formula: Apply the square of a binomial formula to expand (3c + 3)^2. (a + b)^2 = a^2 + 2ab + b^2 (3c + 3)^2 = (3c)^2 + 2(3c)(3) + 3^2Simplification: Simplify (3c)^2 + 2(3c)(3) + 3^2. (3c)^2 + 2(3c)(3) + 3^2 = (3c * 3c) + (2 * 3 * 3)c + 3 * 3 = 9c^2 + 18c + 9

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

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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

(3c + 3)^2

Special Case Identification: We are asked to find the square of the binomial $(3c + 3)$ . This means we need to calculate $(3c + 3)^2$ . $\newline$ Which special case applies here? $\newline$ $(3c + 3)^2$ 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 $b$ . Compare $(3c + 3)^2$ with $(a + b)^2$ . $a = 3c$ $b = 3$
Application of Binomial Formula: Apply the square of a binomial formula to expand $(3c + 3)^2$ . $(a + b)^2 = a^2 + 2ab + b^2$ $(3c + 3)^2 = (3c)^2 + 2(3c)(3) + 3^2$
Simplification: Simplify $(3c)^2 + 2(3c)(3) + 3^2.$ $(3c)^2 + 2(3c)(3) + 3^2$ $= (3c \times 3c) + (2 \times 3 \times 3)c + 3 \times 3$ $= 9c^2 + 18c + 9$