Expand the expression to a polynomial in standard form:

Question

left parenthesis, 4, x, plus, 3, right parenthesis, left parenthesis, minus, 3, x, squared, minus, 5, x, plus, 10, right parenthesis
(4x+3)(−3x
2
−5x+10)

Solve the problem just like the example below
⬇️
Expand the expression to a polynomial in standard form:
left parenthesis, 4, x, minus, 3, right parenthesis, left parenthesis, 2, x, squared, minus, 2, x, minus, 5, right parenthesis

(4x−3)(2x
2
−2x−5)

Combine like terms:
8x³- 14x²-14x+15

Answer 1

Let's expand the expression \((4x + 3)(-3x^2 - 5x + 10)\) and then combine like terms.

First, we will distribute \((4x + 3)\) across each term in \((-3x^2 - 5x + 10)\).

1. Distributing \(4x\) across \((-3x^2 - 5x + 10)\):

   • \(4x \cdot (-3x^2) = -12x^3\)
   • \(4x \cdot (-5x) = -20x^2\)
   • \(4x \cdot 10 = 40x\)

2. Distributing \(3\) across \((-3x^2 - 5x + 10)\):

   • \(3 \cdot (-3x^2) = -9x^2\)
   • \(3 \cdot (-5x) = -15x\)
   • \(3 \cdot 10 = 30\)

Now, we will combine all the terms from the two distributions:

• The \(x^3\) term: \(-12x^3\)
• The \(x^2\) terms: \(-20x^2 - 9x^2 = -29x^2\)
• The \(x\) terms: \(40x - 15x = 25x\)
• The constant term: \(30\)

Putting it all together, we get the polynomial in standard form:

\[ -12x^3 - 29x^2 + 25x + 30 \]

So the final answer, in standard form, is:

\[ -12x^3 - 29x^2 + 25x + 30 \]