Answer:
c = 8
Step-by-step explanation:
Given equation:
[tex]-20x^2+25x^2y-40x=-5x(4x-5xy+c)[/tex]
To find the value of c in the given equation, we can start by simplifying the right side of the equation and then equating the coefficients of similar terms on both sides.
First, distribute -5x on the right side:
[tex]\begin{aligned}-20x^2+25x^2y-40x&=-5x(4x-5xy+c)\\\\&=-5x(4x)-5x(-5xy)-5x(c)\\\\&=-20xx+25xxy-5cx\\\\&=-20x^2+25x^2y-5cx\end{aligned}[/tex]
Therefore:
[tex]-20x^2+25x^2y-40x=-20x^2+25x^2y-5cx[/tex]
We can see that the coefficients of the x² and x²y terms are the same on both sides of the equation.
The coefficient of the x-term on the left side is -40, whereas the coefficient of the x-term on the right side is -5c. Therefore, to find the value of c, we can equate them:
[tex]-40=-5c[/tex]
Now, solve for c by dividing both sides by -5:
[tex]\dfrac{-40}{-5}=\dfrac{-5c}{-5}[/tex]
[tex]8=c[/tex]
So, the value of c is:
[tex]\huge\boxed{\boxed{c=8}}[/tex]
