To expand the expression \((2x+5)(2x^2+x-3)\), we will use the distributive property (also known as the FOIL method for binomials, but in this case, we have a binomial multiplied by a trinomial).
Let's distribute \(2x\) and \(5\) across the trinomial \(2x^2+x-3\):
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Distributing \(2x\): \[ 2x \cdot 2x^2 = 4x^3 \] \[ 2x \cdot x = 2x^2 \] \[ 2x \cdot (-3) = -6x \]
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Distributing \(5\): \[ 5 \cdot 2x^2 = 10x^2 \] \[ 5 \cdot x = 5x \] \[ 5 \cdot (-3) = -15 \]
Now, we combine all the results:
\[ 4x^3 + 2x^2 - 6x + 10x^2 + 5x - 15 \]
Next, we combine like terms:
- The \(x^2\) terms: \(2x^2 + 10x^2 = 12x^2\)
- The \(x\) terms: \(-6x + 5x = -1x\) or \(-x\)
Putting all together, we have:
\[ 4x^3 + 12x^2 - x - 15 \]
So, the final expanded expression in standard form is:
\[ \boxed{4x^3 + 12x^2 - x - 15} \]
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