Expanding Brackets - Corbettmaths

Summary

This video explains how to expand algebraic expressions involving brackets. The process involves multiplying each term inside the bracket by the term outside. Examples include expanding expressions like 4(x + 2), 9(x - 9), and more. The video also covers special cases, such as expanding expressions with negative numbers outside the bracket. The key takeaway is to carefully apply multiplication for each term, paying attention to signs, especially when a negative number is involved. By following these steps, viewers can easily expand algebraic expressions and simplify their work.

Takeaways

• 😀 Expanding brackets involves multiplying the terms inside the bracket by the term outside.
• 😀 For example, 4(x + 2) becomes 4x + 8 after expanding.
• 😀 When expanding, ensure you multiply each term inside the bracket by the number outside.
• 😀 If there is a positive number outside the bracket, you can simply multiply and add terms directly (e.g., 9(x - 9) becomes 9x - 81).
• 😀 Be cautious when there’s a negative number outside the bracket, as it will affect the signs inside (e.g., -5(2x + 3) becomes -10x - 15).
• 😀 The method is the same for letters, where x(x + 3) becomes x^2 + 3x.
• 😀 Always multiply both terms inside the bracket by the number outside.
• 😀 For negative numbers, multiplying two negatives results in a positive (e.g., -3(-2x - 5) becomes 6x + 15).
• 😀 The key concept is consistent: multiply everything inside the bracket by the term outside.
• 😀 The sign of the term outside the bracket directly influences the signs of the resulting expanded terms.

Q & A

What is the general method for expanding brackets?

To expand brackets, you multiply each term inside the bracket by the term outside the bracket.

How would you expand 4(x + 2)?

Multiply 4 by both x and 2. 4 * x = 4x, and 4 * 2 = 8, so the expanded form is 4x + 8.

What happens when you have a negative number outside the bracket?

When a negative number is outside the bracket, you need to multiply each term inside the bracket by the negative number, paying close attention to signs.

How do you expand 9(x - 9)?

Multiply 9 by both x and -9. 9 * x = 9x, and 9 * -9 = -81, so the expanded form is 9x - 81.

What is the expanded form of 9(9x + 4)?

Multiply 9 by both 9x and 4. 9 * 9x = 81x, and 9 * 4 = 36, so the expanded form is 81x + 36.

How do you expand x(x + 3)?

Multiply x by both x and 3. x * x = x², and x * 3 = 3x, so the expanded form is x² + 3x.

What happens when a variable is multiplied by itself, like in x(x)?

When a variable is multiplied by itself, it becomes squared. For example, x * x = x².

How would you expand -5(2x + 3)?

Multiply -5 by both 2x and 3. -5 * 2x = -10x, and -5 * 3 = -15, so the expanded form is -10x - 15.

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

Multiply -3 by both 2x and -5. -3 * 2x = -6x, and -3 * -5 = +15, so the expanded form is -6x + 15.

When multiplying a negative number by a negative number, what happens to the sign?

When you multiply two negative numbers, the result is positive. For example, -3 * -5 = +15.