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

Identify Expression and Identity: Identify the expression to be squared and the relevant algebraic identity. The expression to be squared is (3w + 2). The relevant algebraic identity for squaring a binomial is (a + b)^2 = a^2 + 2ab + b^2.Determine 'a' and 'b': Determine the values of 'a' and 'b' in the identity. In the expression (3w + 2), 'a' is 3w and 'b' is 2.Apply Algebraic Identity: Apply the algebraic identity to the expression (3w + 2)^2. Using the identity (a + b)^2 = a^2 + 2ab + b^2, we get: (3w + 2)^2 = (3w)^2 + 2*(3w)*(2) + (2)^2.Calculate Expanded Expression: Calculate each term of the expanded expression. (3w)^2 = 9w^2, 2*(3w)*(2) = 12w, (2)^2 = 4.Combine Calculated Terms: Combine the calculated terms to get the final simplified expression. 9w^2 + 12w + 4 is the simplified form of (3w + 2)^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.

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(3w + 2)^2

Identify Expression and Identity: Identify the expression to be squared and the relevant algebraic identity. $\newline$ The expression to be squared is $(3w + 2)$ . The relevant algebraic identity for squaring a binomial is $(a + b)^2 = a^2 + 2ab + b^2$ .
Determine 'a' and 'b': Determine the values of 'a' and 'b' in the identity. $\newline$ In the expression $(3w + 2)$ , 'a' is $3w$ and 'b' is $2$ .
Apply Algebraic Identity: Apply the algebraic identity to the expression $(3w + 2)^2$ . Using the identity $(a + b)^2 = a^2 + 2ab + b^2$ , we get: $(3w + 2)^2 = (3w)^2 + 2\cdot(3w)\cdot(2) + (2)^2$ .
Calculate Expanded Expression: Calculate each term of the expanded expression. $\newline$ $(3w)^2 = 9w^2$ , $\newline$ $2\cdot(3w)\cdot(2) = 12w$ , $\newline$ $(2)^2 = 4$ .
Combine Calculated Terms: Combine the calculated terms to get the final simplified expression. $9w^2 + 12w + 4$ is the simplified form of $(3w + 2)^2$ .