Perfect Squares and Middle Terms

The video tutorial explains how to factor the expression 25x^4 - 30x^2 + 9 by recognizing it as a perfect square trinomial. It begins by identifying the perfect squares in the expression and confirms that it can be expressed as the square of a binomial. The tutorial then calculates the middle term to verify the binomial and rewrites the expression as a perfect square, demonstrating the process step-by-step.

What makes the expression 25x^4 - 30x^2 + 9 initially seem challenging to factor?

• The presence of a constant term

• The presence of a fourth power term

• The presence of a cubic term

• The presence of a linear term

Which of the following is a perfect square in the expression 25x^4 - 30x^2 + 9?

• 15x^2

• 25x^4

• 45x^2

• 30x^2

What must the middle term be in order to confirm the expression as a perfect square?

• The sum of the squares of the end terms

• The difference of the squares of the end terms

• Half the product of the square roots of the end terms

• Twice the product of the square roots of the end terms

What is the correct value of the middle term when calculated using 5x^2 and -3?

• 30x^2

• -30x^2

• 15x^2

• -15x^2

How can the expression 25x^4 - 30x^2 + 9 be rewritten as a perfect square?

• (5x^2 - 9)^2

• (5x^2 + 9)^2

• (5x^2 - 3)^2

• (5x^2 + 3)^2