Factoring a perfect square trinomial with two variables

The video tutorial explains how to factor a polynomial expression. It begins by introducing the problem and discussing the strategy for factoring. The teacher identifies numbers that multiply to give a specific product and add to a specific sum. The factors are verified for correctness, and the final form of the expression is written. The tutorial concludes with a reminder to practice writing expressions in the correct form.

What is the first step in factoring the polynomial X^4 + X^4Y^4 - 8X^2Y^2 + 16?

• Check for common factors among the terms

• Multiply all terms by 2

• Add 5 to each term

• Divide each term by X

Which two numbers multiply to 16 and add to -8?

• -4 and -4

• 4 and 4

• -2 and -8

• 2 and 8

What is the correct factorization of the expression X^4 + X^4Y^4 - 8X^2Y^2 + 16?

• (X^2Y^2 - 2)(X^2Y^2 - 8)

• (X^2Y^2 + 4)(X^2Y^2 + 4)

• (X^2Y^2 - 4)(X^2Y^2 - 4)

• (X^2Y^2 + 2)(X^2Y^2 + 8)

What should be verified after factoring the polynomial?

• The terms are all positive

• The multiplication of terms results in the original polynomial

• The polynomial is simplified to a single term

• The polynomial is divided by 2

Why is it important to write the expression in the correct form after factoring?

• To ensure clarity and correctness

• To add more terms

• To confuse the students

• To make it look more complex