Understanding Binomial Multiplication and Patterns

The video tutorial explores solving the expression x + 3 * x - 3 using the distributive property. It demonstrates the step-by-step process of applying the distributive property twice to simplify the expression. The tutorial identifies a pattern where middle terms cancel out, leading to a general formula for expressions of the form x + a * x - a. The video concludes by applying this pattern to other binomials, highlighting the efficiency of recognizing such patterns in algebraic expressions.

What is the first step in solving x + 3 * x - 3 using the distributive property?

• Multiply x by 3

• Multiply x + 3 by x

• Multiply x by -3

• Multiply x + 3 by -3

What is the purpose of applying the distributive property twice in binomial multiplication?

• To simplify the expression

• To find the square of the binomial

• To factor the expression

• To eliminate variables

What is the result of multiplying x by x in the expression x + 3 * x - 3?

• 3x

• x^2

• 9

• x^3

What is the result of multiplying -3 by 3 in the expression x + 3 * x - 3?

• 6

• -6

• 9

• -9

What is the result of x * 3 in the expression x + 3 * x - 3?

• 3x

• x^3

• 9

• x^2

What happens to the middle terms when you add and subtract the same number in a binomial expression?

• They become negative

• They remain unchanged

• They double

• They cancel out

In the expression x + a * x - a, what is the result of a * a?

• a^2

• 2a

• 0

• a

What is the simplified form of x + a * x - a?

• x^2 + a^2

• x^2 - a^2

• x^2 + 2a

• x^2 - 2a

What is the special case formula for binomials of the form x + a * x - a?

• x^2 + a^2

• x^2 - 2a

• x^2 - a^2

• x^2 + 2a

How can you quickly find the product of x + 10 * x - 10 using the special case formula?

• x^2 - 20

• x^2 + 100

• x^2 - 100

• x^2 + 20