Given:
The given expression is [tex]a^2x^2-2cx^2+a^2y-2cy[/tex]
We need to determine the expression that is equivalent to the given expression.
Equivalent expression:
The equivalent expression can be determined by solving the expression.
Let us solve the polynomial function by factoring.
First, we shall group the expression.
Thus, we get;
[tex]x^2(a^2-2c)+y(a^2-2c)[/tex]
Factoring out the common term [tex](a^2-2c)[/tex], we get;
[tex](x^2+y)(a^2-2c)[/tex]
Thus, the expression that is equivalent to the expression [tex]a^2x^2-2cx^2+a^2y-2cy[/tex] is [tex](x^2+y)(a^2-2c)[/tex]
Hence, the equivalent expression is [tex](x^2+y)(a^2-2c)[/tex]
Therefore, Option C is the correct answer.
