Question

select the correct answer. simplify the following polynomial expression. 3x(4x + 5) - 4(-x - 3)(2x - 5) 20x² + 59x - 15 4x² + 59x + 60 20x² + 19x - 60 4x² + 19x + 15

Explanation:

Step1: Expand the first - term

Use the distributive property \(a(b + c)=ab+ac\). So, \(3x(4x + 5)=3x\times4x+3x\times5 = 12x^{2}+15x\).

Step2: Expand the second - term

First, expand \((-x - 3)(2x - 5)\) using the FOIL method \((a + b)(c + d)=ac+ad+bc+bd\). Here, \(a=-x\), \(b = - 3\), \(c = 2x\), \(d=-5\).
\((-x - 3)(2x - 5)=-x\times2x+(-x)\times(-5)+(-3)\times2x+(-3)\times(-5)=-2x^{2}+5x-6x + 15=-2x^{2}-x + 15\).
Then, \(4(-x - 3)(2x - 5)=4(-2x^{2}-x + 15)=-8x^{2}-4x + 60\).

Step3: Combine the two expanded terms

\(3x(4x + 5)-4(-x - 3)(2x - 5)=(12x^{2}+15x)-(-8x^{2}-4x + 60)\).
Remove the parentheses: \(12x^{2}+15x + 8x^{2}+4x-60\).
Combine like - terms: \((12x^{2}+8x^{2})+(15x + 4x)-60=20x^{2}+19x-60\).

Answer:

The correct answer is \(20x^{2}+19x - 60\).