To multiply the expression \((6x + 5y)(-3x + 2y)\), we can apply the distributive property (also known as the FOIL method for binomials). Let's proceed step by step:
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Distribute \(6x\):
- \(6x \cdot (-3x) = -18x^2\)
- \(6x \cdot 2y = 12xy\)
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Distribute \(5y\):
- \(5y \cdot (-3x) = -15xy\)
- \(5y \cdot 2y = 10y^2\)
Now, we combine all these products:
\[ -18x^2 + 12xy - 15xy + 10y^2 \]
Next, combine like terms:
\[ -18x^2 + (12xy - 15xy) + 10y^2 = -18x^2 - 3xy + 10y^2 \]
So, the final expression is:
\[ -18x^2 - 3xy + 10y^2 \]
It appears that none of the choices you provided exactly match this result, but it seems I may have misaligned my expectation with your original query.
However, based on the calculations, the correct answer should be:
\(-18x^2 - 3xy + 10y^2\)
If the choices should have included this, you could check them again. If we had made a mistake earlier in reading your options, please clarify or check.
1 answer