Questions: (2y-3)^2

Transcript text: 13. $(2 y-3)^{2}$

Solution

Solution Steps

Step 1: Define the Expression

We start with the expression $(2y - 3)^{2}$.

Step 2: Apply the Binomial Expansion

Using the formula for the square of a binomial, we expand the expression: \[ (2y - 3)^{2} = (2y)^{2} - 2 \cdot (2y) \cdot 3 + 3^{2} \]

Step 3: Simplify the Expression

Calculating each term, we have: \[ (2y)^{2} = 4y^{2}, \quad -2 \cdot (2y) \cdot 3 = -12y, \quad \text{and} \quad 3^{2} = 9 \] Combining these results gives us: \[ (2y - 3)^{2} = 4y^{2} - 12y + 9 \]

Final Answer

$\boxed{4y^{2} - 12y + 9}$

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