Simplifying Expressions and Binomials

The video tutorial covers simplifying square roots, emphasizing the importance of reducing numbers under the root for simplicity. It explains the distributive property, showing how multiplication affects terms within brackets. Finally, it demonstrates expanding binomials, highlighting the interaction between terms and the resulting expressions.

What is the simplified form of the square root of 96?

• 4√6

• 12√2

• 8√3

• 6√4

Why is it beneficial to have a smaller number under the square root?

• It has no effect on the expression.

• It makes calculations more complex.

• It simplifies the expression.

• It increases the value of the expression.

What happens when you multiply a number outside the brackets with each term inside the brackets?

• Only the first term is multiplied.

• The number outside the brackets is subtracted from each term.

• All terms inside the brackets are multiplied.

• The number outside the brackets is added to each term.

What is the result of simplifying the expression 3(a + 4)?

• 3a + 7

• a + 12

• 3a + 12

• 3a + 4

What is a common mistake when expanding expressions with negative signs?

• Ignoring the negative sign.

• Incorrectly distributing the negative sign across all terms.

• Multiplying only the first term by the negative sign.

• Adding the negative sign to each term.

What is the correct way to handle a negative sign in front of a bracketed expression?

• Ignore the negative sign.

• Apply the negative sign to only the first term.

• Apply the negative sign to each term inside the brackets.

• Add the negative sign to the expression.

What is the simplified form of 1 - 2(x + 5)?

• 1 - 2x - 10

• -2x + 5

• 1 - 2x + 10

• -2x - 9

What is the expanded form of (c + 7)²?

• c² + 7c + 49

• c² + 2c + 49

• c² + 14c + 49

• c² + 49

How do the terms in a squared binomial interact?

• They cancel each other out.

• They interact to form a middle term.

• They are multiplied independently.

• They are added separately.

What additional term is added when expanding (c + 7)²?

• 49c

• 14c

• 7c

• 21c