Understanding Binomial Expansion

The video tutorial explains how to correctly expand the expression (7x + 10)^2. It begins by highlighting a common mistake where people incorrectly square each term separately. The correct approach involves recognizing (7x + 10)^2 as (7x + 10)(7x + 10) and using the distributive property to expand it. The tutorial further generalizes this method for any binomial (a + b)^2, showing that it results in a^2 + 2ab + b^2. Finally, the method is applied to the specific problem, resulting in the expanded form 49x^2 + 140x + 100.

What is a common mistake when expanding (7x + 10)^2?

• Multiplying the terms correctly

• Squaring each term individually

• Using the distributive property

• Applying the FOIL method

Why is it incorrect to expand (7x + 10)^2 as (7x)^2 + 10^2?

• Because it multiplies the terms correctly

• Because it applies the distributive property

• Because it uses the FOIL method

• Because it ignores the middle term

What is the correct expression for (a + b)^2?

• a^2 + b^2

• a^2 + 2ab + b^2

• a^2 + ab + b^2

• a^2 + 2a + b^2

What is the result of applying the distributive property to (a + b)(a + b)?

• a^2 + 2ab + b^2

• a^2 + b^2

• a^2 + ab + b^2

• a^2 + 2a + b^2

What is the purpose of using the distributive property in binomial expansion?

• To simplify the expression

• To find the middle term

• To ensure all terms are multiplied

• To square each term individually

How do you calculate the middle term in the expansion of (7x + 10)^2?

• By adding 7x and 10

• By squaring 10

• By squaring 7x

• By multiplying 7x and 10 and doubling the result

What is the expanded form of (7x + 10)^2?

• 49x^2 + 100

• 49x^2 + 140x + 100

• 49x^2 + 70x + 100

• 49x^2 + 10x + 100

What is the value of 7 squared in the expression (7x + 10)^2?

• 70

• 21

• 49

• 14

What is the final term in the expansion of (7x + 10)^2?

• 10

• 20

• 100

• 200

What is the coefficient of the x term in the expansion of (7x + 10)^2?

• 49

• 70

• 140

• 100