Answer :
The only statement or equation that is correct from the given equation is [tex]35g^5-25g^2=5g^2(7g^3-5)[/tex].
What is an equation?
An equation is formed of two expressions which are equated together with the help of an equal sign.
In order to check which of the statements are true, we will solve the right side of each of the equations and compare it with the corresponding left side of the equation.
A.) [tex]24g^4+18g^2=6g^2(4g^2+3g)[/tex]
Solving the right side of the equation, therefore, we will get the value,
[tex]=6g^2(4g^2+3g)\\\\=24g^4+18g^3[/tex]
As we can see on solving the right side of the equation it is not equal to the left side of the equation.
Thus, the equation is not correct.
B.) [tex]35g^5-25g^2=5g^2(7g^3-5)[/tex]
Solving the right side of the equation, therefore, we will get the value,
[tex]=5g^2(7g^3-5)\\\\=36g^5-25g^2[/tex]
As we can see that both sides of the equation are equal.
Thus, the equation is correct.
C.) [tex]9g^3+12=3(3g^3+4) 4g^2-g=g^2(4-g)[/tex]
As the equation has three different expressions, therefore, solving the second and the third expression, we will get
[tex]=3(3g^3+4) 4g^2-g\\\\= (9g^3+12) 4g^2-g\\\\=36g^5+48g^2-g\\\\[/tex]
As we can see on solving the second expression itself the equation is not equal to the left side of the equation.
Thus, the equation is not correct.
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