Answer:
Option (c) is correct.
The simplified form of \((2x^2+4x-3)(3x+1)\) is \(6x^3+14x^2-5x-3\)
Step-by-step explanation:
Given : \((2x^2+4x-3)(3x+1)\)
We have to write the given product in simplified form and choose correct option from the given options.
Consider \(\left(2x^2+4x-3\right)\left(3x\:+1\right)\)
Multiply each term of first bracket with each term of second bracket, we get,
\(=2x^2\cdot \:3x+2x^2\cdot \:1+4x\cdot \:3x+4x\cdot \:1+\left(-3\right)\cdot \:3x+\left(-3\right)\cdot \:1\)
Apply minus plus rule \(+\left(-a\right)=-a\) , we get,
\(=2\cdot \:3x^2x+2\cdot \:1\cdot \:x^2+4\cdot \:3xx+4\cdot \:1\cdot \:x-3\cdot \:3x-3\cdot \:1\)
On simplifying, we get,
Adding similar terms,
\(4x-9x=-5x\\\\\\ and\ 2x^2+12x^2=14x^2\)
\(=6x^3+14x^2-5x-3\)
Thus, option (c) is correct.
The simplified form of \((2x^2+4x-3)(3x+1)\) is \(6x^3+14x^2-5x-3\)
