Expand the expression to a polynomial in standard form:

Question

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

Answer 1

To expand the expression \((4x + 5)(x^2 - 2x + 5)\), we'll use the distributive property (also known as the FOIL method for binomials).

1. Start by distributing \(4x\) to each term in the second parentheses: \[ 4x \cdot x^2 = 4x^3 \] \[ 4x \cdot (-2x) = -8x^2 \] \[ 4x \cdot 5 = 20x \]

2. Now, distribute \(5\) to each term in the second parentheses: \[ 5 \cdot x^2 = 5x^2 \] \[ 5 \cdot (-2x) = -10x \] \[ 5 \cdot 5 = 25 \]

3. Now, combine all these results together: \[ 4x^3 - 8x^2 + 20x + 5x^2 - 10x + 25 \]

4. Combine like terms:

   • For \(x^2\) terms: \(-8x^2 + 5x^2 = -3x^2\)
   • For \(x\) terms: \(20x - 10x = 10x\)

Putting it all together, we have: \[ 4x^3 - 3x^2 + 10x + 25 \]

Thus, the expanded expression in standard form is: \[ \boxed{4x^3 - 3x^2 + 10x + 25} \]