Questions: (5x-2y)(3x+4y)

(5x-2y)(3x+4y)
Transcript text: $(5 x-2 y)(3 x+4 y)$
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Solution

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Solution Steps

Step 1: Expand the Expression

We start with the expression \((5x - 2y)(3x + 4y)\). To expand it, we apply the distributive property (FOIL method):

\[ (5x)(3x) + (5x)(4y) + (-2y)(3x) + (-2y)(4y) \]

Step 2: Calculate Each Term

Calculating each term gives us:

\[ 15x^2 + 20xy - 6xy - 8y^2 \]

Step 3: Combine Like Terms

Now, we combine the like terms \(20xy\) and \(-6xy\):

\[ 15x^2 + (20xy - 6xy) - 8y^2 = 15x^2 + 14xy - 8y^2 \]

Thus, the expanded form of the expression \((5x - 2y)(3x + 4y)\) is:

\[ 15x^2 + 14xy - 8y^2 \]

Final Answer

\(\boxed{15x^2 + 14xy - 8y^2}\)

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