Carrillo Harris
08/08/2023 · Middle School
\( 1 \leftarrow \quad \) Multiply using one of the rules for the square of a binomial. \[ \begin{array}{l}(5 x-6 y)^{2} \\ (5 x-6 y)^{2}=\square\end{array} \]
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Step-by-step Solution
To multiply \((5x - 6y)^2\) using the square of a binomial formula, we can use the identity:
\[
(a - b)^2 = a^2 - 2ab + b^2
\]
In this case, let \(a = 5x\) and \(b = 6y\). Now we can apply the formula:
1. Calculate \(a^2\):
\[
(5x)^2 = 25x^2
\]
2. Calculate \(b^2\):
\[
(6y)^2 = 36y^2
\]
3. Calculate \(2ab\):
\[
2(5x)(6y) = 60xy
\]
Now, substituting these values into the formula gives us:
\[
(5x - 6y)^2 = a^2 - 2ab + b^2 = 25x^2 - 60xy + 36y^2
\]
Thus, we can write:
\[
(5x - 6y)^2 = 25x^2 - 60xy + 36y^2
\]
So, the final answer is:
\[
(5x - 6y)^2 = 25x^2 - 60xy + 36y^2
\]
Quick Answer
\[
(5x - 6y)^2 = 25x^2 - 60xy + 36y^2
\]
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