Expanding Expressions and Brackets

This video tutorial explains how to expand single brackets in algebraic expressions. It begins with a basic method of adding terms and then introduces a more efficient technique using multiplication. The tutorial covers examples with different numbers of terms inside the brackets and concludes with a final example to reinforce the concept.

What does it mean to expand a single bracket with one term outside and multiple terms inside?

• To divide the term outside by each term inside

• To subtract the terms inside the bracket

• To add the terms inside the bracket

• To multiply the term outside with each term inside

How can you expand the expression 3(2x + 3y) by adding terms?

• By subtracting 2x + 3y three times

• By adding 2x + 3y three times

• By multiplying 3 with 2x and 3y

• By dividing 2x + 3y by 3

What is the result of expanding 3(2x + 3y) using the quicker method?

• 6x + 9y

• 3x + 6y

• 5x + 8y

• 4x + 7y

Why is the quicker method preferred for expanding brackets?

• It uses fewer steps

• It avoids multiplication

• It is faster and more efficient

• It is more accurate

When using the quicker method, what is the first step in expanding 5a(4a - 3b + 6)?

• Add all terms inside the bracket

• Divide 5a by each term inside the bracket

• Multiply 5a by each term inside the bracket

• Subtract 5a from each term inside the bracket

What is the expanded form of 5a(4a - 3b + 6)?

• 20a^2 - 15ab + 30a

• 20a^2 + 15ab - 30a

• 20a^2 - 15ab - 30a

• 20a^2 + 15ab + 30a

What is the purpose of using arrows when expanding expressions like 5a(4a - 3b + 6)?

• To mark addition

• To highlight multiplication

• To show division

• To indicate subtraction

In the final example, what is the first step when the bracket is only multiplied by 3?

• Subtract 3 from x and -5

• Add 3 to x and -5

• Multiply 3 by x and -5

• Divide 3 by x and -5

What is the expanded form of 3(x - 5) when the 2x term is separate?

• 2x - 3x - 15

• 2x - 3x + 15

• 2x + 3x - 15

• 2x + 3x + 15

After expanding and simplifying 2x + 3(x - 5), what is the final result?

• 5x + 15

• 5x - 10

• 5x - 15

• 5x + 10