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

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

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Find the square. Simplify your answer. $\newline$ $(2v + 3)^2$

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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

(2v + 3)^2

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