Expand the expression to a polynomial in standard form:

Question

left parenthesis, 2, x, plus, 5, right parenthesis, left parenthesis, 2, x, squared, plus, x, minus, 3, right parenthesis
(2x+5)(2x
2
+x−3)

Answer 1

To expand the expression \((2x + 5)(2x^2 + x - 3)\), we will use the distributive property (also known as the FOIL method for binomials).

1. Distribute \(2x\) to each term in the second polynomial: \[ 2x \cdot 2x^2 = 4x^3 \] \[ 2x \cdot x = 2x^2 \] \[ 2x \cdot (-3) = -6x \]

2. Now distribute \(5\) to each term in the second polynomial: \[ 5 \cdot 2x^2 = 10x^2 \] \[ 5 \cdot x = 5x \] \[ 5 \cdot (-3) = -15 \]

3. Now combine all these results: \[ 4x^3 + 2x^2 - 6x + 10x^2 + 5x - 15 \]

4. Combine like terms:

   • For \(x^2\): \(2x^2 + 10x^2 = 12x^2\)
   • For \(x\): \(-6x + 5x = -x\)

5. So we can now write the polynomial in standard form, combining all the like terms: \[ 4x^3 + 12x^2 - x - 15 \]

Thus, the expanded polynomial in standard form is: \[ \boxed{4x^3 + 12x^2 - x - 15} \]