Exploring Adding and Subtracting Rational Expressions

The video tutorial begins with warm-up questions involving multiplication and simplification of expressions. It introduces the concept of the difference of squares, highlighting patterns in perfect squares. The tutorial then transitions to factoring using the greatest common factor (GCF), demonstrating how to simplify expressions by identifying and dividing by the GCF. Throughout, the instructor emphasizes recognizing patterns and applying mathematical operations to solve problems effectively.

What is the result of multiplying x by x?

• x

• x^2

• 2x

• x^3

What do you get when you multiply 4 by -4?

• 0

• 16

• -16

• -8

What is the simplified form of 25x^2 - 1?

• (25x + 1)(x - 1)

• (5x - 1)^2

• (5x + 1)^2

• (5x + 1)(5x - 1)

What is the result of multiplying 2a by 2a?

• 4a^2

• 4a

• 2a^2

• 8a^2

What is the simplified form of 4a^2 - 9b^2?

• (2a + 3b)^2

• (4a - 9b)^2

• (2a + 3b)(2a - 3b)

• (4a + 9b)(4a - 9b)

What is the square root of 81?

• 9

• 8

• 7

• 10

What is the square root of 100?

• 11

• 10

• 9

• 8

What is the first step in factoring any expression?

• Subtract the terms

• Multiply the terms

• Add the terms

• Find the GCF

What is the GCF of 32 and 18?

• 8

• 2

• 4

• 6

What is the simplified form of 16x^2 - 9u^2?

• (16x - 9u)^2

• (4x + 3u)(4x - 3u)

• (16x + 9u)(16x - 9u)

• (4x + 3u)^2