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

Special Case Identification: We are asked to find the square of the binomial (2r - 3). This means we need to calculate (2r - 3)^2. Which special case applies here? (2r - 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 (2r - 3)^2 with (a - b)^2. a = 2r b = 3Application of Formula: Apply the square of a binomial formula to expand (2r - 3)^2. (a - b)^2 = a^2 - 2ab + b^2 (2r - 3)^2 = (2r)^2 - 2(2r)(3) + (3)^2Simplification: Simplify (2r)^2 - 2(2r)(3) + (3)^2. (2r)^2 - 2(2r)(3) + (3)^2 = (2r * 2r) - (2 * 2 * 3)r + 3 * 3 = 4r^2 - 12r + 9

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Find the square. Simplify your answer. $\newline$ $(2r - 3)^2$

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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

(2r - 3)^2

Special Case Identification: We are asked to find the square of the binomial $(2r - 3)$ . This means we need to calculate $(2r - 3)^2$ . Which special case applies here? $(2r - 3)^2$ is in the form of $(a - b)^2$ . Special case: $(a - b)^2 = a^2 - 2ab + b^2$
Values of a and b: Identify the values of $a$ and $b$ . $\newline$ Compare $(2r - 3)^2$ with $(a - b)^2$ . $\newline$ $a = 2r$ $\newline$ $b = 3$
Application of Formula: Apply the square of a binomial formula to expand $(2r - 3)^2$ . $\newline$ $(a - b)^2 = a^2 - 2ab + b^2$ $\newline$ $(2r - 3)^2 = (2r)^2 - 2(2r)(3) + (3)^2$
Simplification: Simplify $(2r)^2 - 2(2r)(3) + (3)^2.$ $(2r)^2 - 2(2r)(3) + (3)^2$ $= (2r \cdot 2r) - (2 \cdot 2 \cdot 3)r + 3 \cdot 3$ $= 4r^2 - 12r + 9$