Question

Explain why this is wrong:

Answer 1

Answer:

See below.

Step-by-step explanation:

y^2 - 6y + 9 can be changed correctly into y^2 - 2(y)(3) + 3^2.

Up to here, it's correct.

The right side above shows a polynomial that is the square of a binomial.

It factors into (y - 3)^2.

The correct factorization is (y - 3)^2.

The incorrect factorization of the student's solution is the product of a sum and difference.

The product of a sum and a difference is the correct factorization for a difference of squares.

For example, y^2 - 9 is the same as y^2 - 3^2 and is a difference of squares.

It factors into (y + 3)(y - 3), a product of a sum and a difference.