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

Recognize special case: We are asked to find the square of the binomial (2r - 2). The first step is to recognize that this is a special case of the algebraic identity (a - b)^2 = a^2 - 2ab + b^2.Identify values of a and b: Identify the values of a and b in the binomial (2r - 2). By comparing it to the general form (a - b)^2, we can see that a = 2r and b = 2.Apply algebraic identity: Apply the algebraic identity (a - b)^2 = a^2 - 2ab + b^2 to the binomial (2r - 2) using the identified values of a and b. (2r - 2)^2 = (2r)^2 - 2*(2r)*(2) + (2)^2Simplify each term: Simplify each term in the expression (2r)^2 - 2*(2r)*(2) + (2)^2. (2r)^2 = 4r^2 2*(2r)*(2) = 8r (2)^2 = 4 So, (2r - 2)^2 = 4r^2 - 8r + 4

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

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Math Problems

Algebra 1

Multiply two binomials: special cases

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Q. Find the square. Simplify your answer.

\newline

(2r - 2)^2

Recognize special case: We are asked to find the square of the binomial $(2r - 2)$ . The first step is to recognize that this is a special case of the algebraic identity $(a - b)^2 = a^2 - 2ab + b^2$ .
Identify values of $a$ and $b$ : Identify the values of $a$ and $b$ in the binomial $(2r - 2)$ . By comparing it to the general form $(a - b)^2$ , we can see that $a = 2r$ and $b = 2$ .
Apply algebraic identity: Apply the algebraic identity $(a - b)^2 = a^2 - 2ab + b^2$ to the binomial $(2r - 2)$ using the identified values of $a$ and $b$ . $(2r - 2)^2 = (2r)^2 - 2\cdot(2r)\cdot(2) + (2)^2$
Simplify each term: Simplify each term in the expression $(2r)^2 - 2\cdot(2r)\cdot 2 + (2)^2$ . $(2r)^2 = 4r^2$ $2\cdot(2r)\cdot 2 = 8r$ $(2)^2 = 4$ So, $(2r - 2)^2 = 4r^2 - 8r + 4$