Find the square. Simplify your answer. (3q - 3)^2 ______

Recognize special case: We are asked to find the square of the binomial (3q - 3). The first step is to recognize that this is a special case of the algebraic identity (a - b)^2, which expands to a^2 - 2ab + b^2.Identify values of a and b: Identify the values of a and b in the binomial (3q - 3). By comparing it to the general form (a - b)^2, we can see that a = 3q and b = 3.Apply algebraic identity: Apply the algebraic identity (a - b)^2 = a^2 - 2ab + b^2 to the binomial (3q - 3). (3q - 3)^2 = (3q)^2 - 2(3q)(3) + (3)^2Simplify each term: Simplify each term in the expression (3q)^2 - 2(3q)(3) + (3)^2. (3q)^2 = 9q^2 (since (3q) * (3q) = 9q^2) 2(3q)(3) = 18q (since 2 * 3q * 3 = 18q) (3)^2 = 9 (since 3 * 3 = 9)Combine simplified terms: Combine the simplified terms to get the final expanded and simplified form of the square of the binomial (3q - 3). (3q - 3)^2 = 9q^2 - 18q + 9

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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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(3q - 3)^2

Recognize special case: We are asked to find the square of the binomial $(3q - 3)$ . The first step is to recognize that this is a special case of the algebraic identity $(a - b)^2$ , which expands to $a^2 - 2ab + b^2$ .
Identify values of $a$ and $b$ : Identify the values of $a$ and $b$ in the binomial $(3q - 3)$ . By comparing it to the general form $(a - b)^2$ , we can see that $a = 3q$ and $b = 3$ .
Apply algebraic identity: Apply the algebraic identity $(a - b)^2 = a^2 - 2ab + b^2$ to the binomial $(3q - 3)$ . $(3q - 3)^2 = (3q)^2 - 2(3q)(3) + (3)^2$
Simplify each term: Simplify each term in the expression $(3q)^2 - 2(3q)(3) + (3)^2.$ $(3q)^2 = 9q^2$ (since $(3q) \times (3q) = 9q^2$ ) $2(3q)(3) = 18q$ (since $2 \times 3q \times 3 = 18q$ ) $(3)^2 = 9$ (since $3 \times 3 = 9$ )
Combine simplified terms: Combine the simplified terms to get the final expanded and simplified form of the square of the binomial $(3q - 3)$ . $(3q - 3)^2 = 9q^2 - 18q + 9$