Question

Which expression is equivalent to a2x2-2cx2 +a2y-2cy? (Polynomial Functions - Factoring)

(x2-y)(a2-2c)

(x2-y)(a+c)

(x2+y)(a2-2c)

(x2+y)(a+c)

Show work

Answer 1

Given:

The given expression is
`a^2x^2-2cx^2+a^2y-2cy`

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;

`x^2(a^2-2c)+y(a^2-2c)`

Factoring out the common term
`(a^2-2c)`, we get;

`(x^2+y)(a^2-2c)`

Thus, the expression that is equivalent to the expression
`a^2x^2-2cx^2+a^2y-2cy` is
`(x^2+y)(a^2-2c)`

Hence, the equivalent expression is
`(x^2+y)(a^2-2c)`

Therefore, Option C is the correct answer.