Question

Expand the expression to a polynomial in standard form:
left parenthesis, 2, x, plus, 5, right parenthesis, left parenthesis, x, minus, 2, right parenthesis, left parenthesis, 2, x, plus, 3, right parenthesis
(2x+5)(x−2)(2x+3)




Solve the problem just like the example below
⬇️
Expand the expression to a polynomial in standard form:
left parenthesis, 2, x, plus, 1, right parenthesis, left parenthesis, 3, x, minus, 5, right parenthesis, left parenthesis, 3, x, plus, 1, right parenthesis
(2x+1)(3x−5)(3x+1)
left parenthesis, 2, x, plus, 1, right parenthesis, left parenthesis, 9, x, squared, minus, 12, x, minus, 5, right parenthesis
(2x+1)(9x
2
−12x−5)

9, x, squared
9x
2
minus, 12, x
−12x
minus, 5
−5
2, x
2x
18, x, cubed
18x
3
minus, 24, x, squared
−24x
2
minus, 10, x
−10x
plus, 1
+1
9, x, squared
9x
2
minus, 12, x
−12x
minus, 5
−5
Combine like terms:
Combine like terms:
18, x, cubed, minus, 15, x, squared, minus, 22, x, minus, 5
18x
3
−15x
2
−22x−5

Answer 1

To expand the expression \((2x + 5)(x - 2)(2x + 3)\) and write it in standard form, we will follow these steps:

1. **Expand the first two binomials:**
\[
(2x + 5)(x - 2)
\]
Using the distributive property (FOIL method):
\[
= 2x \cdot x + 2x \cdot (-2) + 5 \cdot x + 5 \cdot (-2)
\]
\[
= 2x^2 - 4x + 5x - 10
\]
\[
= 2x^2 + x - 10
\]

2. **Now, multiply the result by the third binomial \((2x + 3)\):**
\[
(2x^2 + x - 10)(2x + 3)
\]
Again, we will use the distributive property:
\[
= 2x^2 \cdot 2x + 2x^2 \cdot 3 + x \cdot 2x + x \cdot 3 + (-10) \cdot 2x + (-10) \cdot 3
\]
\[
= 4x^3 + 6x^2 + 2x^2 + 3x - 20x - 30
\]

3. **Combine like terms:**
\[
= 4x^3 + (6x^2 + 2x^2) + (3x - 20x) - 30
\]
\[
= 4x^3 + 8x^2 - 17x - 30
\]

4. **Final polynomial in standard form:**
\[
4x^3 + 8x^2 - 17x - 30
\]

So, the expanded expression to a polynomial in standard form is:
\[
\boxed{4x^3 + 8x^2 - 17x - 30}
\]