Certainly! Let's simplify the polynomial step-by-step:
We start with the given polynomial:
[tex]\[ 4x(2x - 3) - 5(3x - 4) \][/tex]
First, we need to distribute the [tex]\(4x\)[/tex] through the first parentheses:
[tex]\[ 4x(2x - 3) = 4x \cdot 2x + 4x \cdot (-3) \][/tex]
[tex]\[ = 8x^2 - 12x \][/tex]
Next, we distribute the [tex]\(-5\)[/tex] through the second parentheses:
[tex]\[ -5(3x - 4) = -5 \cdot 3x + (-5) \cdot (-4) \][/tex]
[tex]\[ = -15x + 20 \][/tex]
Now we combine the results from both distributions:
[tex]\[ 8x^2 - 12x - 15x + 20 \][/tex]
After that, we combine the like terms [tex]\(-12x\)[/tex] and [tex]\(-15x\)[/tex]:
[tex]\[ -12x - 15x = -27x \][/tex]
So the equivalent expression is:
[tex]\[ 8x^2 - 27x + 20 \][/tex]
Therefore, the simplified form of the polynomial is:
[tex]\[ 8x^2 - 27x + 20 \][/tex]
