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

Identify a and b: We are asked to find the square of the binomial (3y - 3). This is in the form of (a - b)^2, which is a special case of binomial expansion. Special case: (a - b)^2 = a^2 - 2ab + b^2Apply binomial formula: Identify the values of a and b in the binomial (3y - 3). Compare (3y - 3)^2 with (a - b)^2. a = 3y b = 3Simplify the expression: Apply the square of a binomial formula to expand (3y - 3)^2. (a - b)^2 = a^2 - 2ab + b^2 (3y - 3)^2 = (3y)^2 - 2(3y)(3) + (3)^2Simplify the expression (3y)^2 - 2(3y)(3) + (3)^2. (3y)^2 - 2(3y)(3) + (3)^2 = (3y * 3y) - (2 * 3 * 3)y + 3 * 3 = 9y^2 - 18y + 9

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Algebra 1

Multiply two binomials: special cases

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Q. Find the square. Simplify your answer.

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(3y - 3)^2

Identify $a$ and $b$ : We are asked to find the square of the binomial $(3y - 3)$ . This is in the form of $(a - b)^2$ , which is a special case of binomial expansion. $\newline$ Special case: $(a - b)^2 = a^2 - 2ab + b^2$
Apply binomial formula: Identify the values of $a$ and $b$ in the binomial $(3y - 3)$ . Compare $(3y - 3)^2$ with $(a - b)^2$ . $a = 3y$ $b = 3$
Simplify the expression: Apply the square of a binomial formula to expand $(3y - 3)^2$ . $\newline$ $(a - b)^2 = a^2 - 2ab + b^2$ $\newline$ $(3y - 3)^2 = (3y)^2 - 2(3y)(3) + (3)^2$
Simplify the expression: Apply the square of a binomial formula to expand $(3y - 3)^2$ . $(a - b)^2 = a^2 - 2ab + b^2$ $(3y - 3)^2 = (3y)^2 - 2(3y)(3) + (3)^2$ Simplify the expression $(3y)^2 - 2(3y)(3) + (3)^2$ . $(3y)^2 - 2(3y)(3) + (3)^2$ $= (3y \times 3y) - (2 \times 3 \times 3)y + 3 \times 3$ $= 9y^2 - 18y + 9$