Factoring Difference of Squares and Perfect Square Trinomials

In this Math Hacks video, Brett introduces fast and easy formulas for factoring quadratics, focusing on perfect squares. The lesson covers factoring the difference of perfect squares and polynomials that factor into binomials squared. Brett explains the formulas and demonstrates their application through examples, including cases with coefficients and more complex expressions. The video concludes with a call to support the channel by liking and subscribing.

Why is factoring quadratics considered a critical algebra skill?

• It simplifies complex algebraic expressions.

• It is essential for understanding calculus.

• It is used in geometry.

• It helps in solving linear equations.

What is the formula for factoring the difference of two perfect squares?

• (ax - B)(ax + B)

• (ax + B)(ax - B)

• (ax + B)(ax + B)

• (ax - B)(ax - B)

In the expression x^2 - 9, what are the values of a and b?

• a = 1, b = 9

• a = 9, b = 1

• a = 3, b = 1

• a = 1, b = 3

How does the factorization of x^2 - 9 look like?

• (x - 9)(x + 9)

• (x - 2)(x + 2)

• (x - 1)(x + 1)

• (x - 3)(x + 3)

What is the first step in factoring 4x^2 - 25?

• Rewrite 4 as 2^2 and 25 as 5^2

• Rewrite 4 as 2^2 and 25 as 25

• Rewrite 4 as 4^2 and 25 as 25^2

• Rewrite 4 as 2 and 25 as 5

How can X^8 be rewritten to fit the perfect square pattern?

• X^4 squared

• X^2 squared

• X^3 squared

• X^6 squared

What is the factorization of X^8 - 1?

• (X^4 - 1)(X^4 + 1)

• (X^2 - 1)(X^2 + 1)

• (X^4 - 1)(X^4 - 1)

• (X^2 - 1)(X^2 - 1)

What is the shortcut for factoring a trinomial with all plus signs?

• Use the formula (aX - B)^2

• Use the formula (aX + B)(aX - B)

• Use the formula (aX + B)^2

• Use the formula (aX - B)(aX + B)

For the trinomial 4x^2 - 12x + 9, what are the values of a and b?

• a = 3, b = 2

• a = 1, b = 3

• a = 2, b = 3

• a = 4, b = 9

What is the factorization of 4x^2 - 12x + 9?

• (2x - 3)^2

• (2x + 3)^2

• (4x - 9)^2

• (4x + 9)^2