Factoring Differences of Squares

The video tutorial explains how to factor the expression 49x^2 - 49y^2 by recognizing it as a difference of squares. It demonstrates the pattern a^2 - b^2 = (a + b)(a - b) and applies it to the given expression. An alternative method is also shown, factoring out the common factor of 49 first, then applying the difference of squares pattern to the remaining expression.

What expression are we trying to factor in this lesson?

• 49x^2 + 49y^2

• 49x^2 - 49y^2

• 7x^2 - 7y^2

• x^2 - y^2

What is the result of multiplying (a + b) by (a - b)?

• a^2 + 2ab + b^2

• a^2 + b^2

• a^2 - b^2

• 2ab

How can 49x^2 be rewritten using a perfect square?

• (14x)^2

• (x)^2

• (49x)^2

• (7x)^2

What is the factored form of 49x^2 - 49y^2 using the pattern a^2 - b^2?

• (7x + y)(7x - y)

• (7x + 7y)(7x - 7y)

• (x + y)(x - y)

• (49x + 49y)(49x - 49y)

What common factor can be extracted from 49x^2 - 49y^2?

• 7

• 49

• y

• x

After factoring out 49, what expression is left to factor?

• x^2 + y^2

• x^2 - y^2

• 49x^2 - 49y^2

• 7x^2 - 7y^2

What is the factored form of x^2 - y^2?

• (x^2 - y^2)

• (x + y)(x - y)

• (x + y)(x + y)

• (x - y)(x - y)

How do the two methods of factoring 49x^2 - 49y^2 compare?

• One is more accurate than the other.

• They cannot be compared.

• They result in different expressions.

• They are equivalent.

What is the result of factoring 49x^2 - 49y^2 using the common factor method?

• 7(x^2 - y^2)

• 7(x + y)(x - y)

• 49(x^2 - y^2)

• 49(x + y)(x - y)

What is the purpose of factoring expressions like 49x^2 - 49y^2?

• To simplify calculations

• To make expressions more complex

• To change the variables

• To eliminate terms