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