(x-2)(3x%2B4).jpeg "(2x+5)(x-2)(3x+4)")
Expanding the Expression (2x+5)(x-2)(3x+4)
This article explores how to expand the given expression (2x+5)(x-2)(3x+4).
Expanding with the Distributive Property
We can expand this expression by using the distributive property multiple times.
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First, expand (2x+5)(x-2):
(2x+5)(x-2) = 2x(x-2) + 5(x-2) = 2x² - 4x + 5x - 10 = 2x² + x - 10
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Now, expand the result from step 1 by (3x+4):
(2x² + x - 10)(3x+4) = 2x²(3x+4) + x(3x+4) - 10(3x+4) = 6x³ + 8x² + 3x² + 4x - 30x - 40 = 6x³ + 11x² - 26x - 40
Therefore, the expanded form of (2x+5)(x-2)(3x+4) is 6x³ + 11x² - 26x - 40.
Additional Notes
- The order of expansion doesn't matter: You could have started by expanding (x-2)(3x+4) and then multiplying the result by (2x+5). The final expanded expression will always be the same.
- FOIL method: You could also use the FOIL method (First, Outer, Inner, Last) to expand the expression two at a time.
- Factoring: Notice that the final expanded expression is a cubic polynomial. It's possible that it can be factored further, but in this case, it's already in its simplest form.