Expanding Brackets single What does Expanding mean With
Expanding Brackets - single
What does Expanding mean?
With numbers This process can be visualised in terms of finding the area of a rectangle Find the area of: 2 5 2 ① ② The area of this rectangle can be worked out by adding the two lengths together (5 + 2) and then multiplying by 2 i. e. 2(5 + 2) =2 x 7 = 14 It could also be worked out by calculating the two individual areas, and then adding these together ① + ② i. e. 2 x 5 + 2 x 2 = 10 + 4 = 14
Variables now included We can apply this same process to an algebraic expression involving a variable y + 2 Find the area of: 2 ① ② This time however, we cannot simply add the y to the 2, so we use the second method from before to work out an expression for the total area of this rectangle i. e. 2(y + 2) ① + ② = 2 x y + 2 x 2 = 2 y + 4
The Distributive Law This process is known as the Distributive Law a(b + c) = axb + axc This is the key idea behind expanding, and applies to both number, algebraic and mixed expressions and equations. When expanding brackets, each term inside the brackets is multiplied by the number outside, then like terms are collected together.
Some examples:
Summarising To simplify an algebraic expression involving brackets: 1. Expand any brackets first (be careful with negatives) 2. Then add or subtract any like terms Note: Having a minus sign in front of the brackets changes the sign of every term inside the brackets
Further examples:
Practice Expand simplify if required: 1. 7(x + y) 2. 2(x – 3) 3. -4(x + 5) 4. -3(x – 6) 5. x(y – 4) 6. -4(5 x – 1) 7. 2 x(3 x – 3) 8. -x(2 – 3 x) 9. 4(2 x - 7) + 3(x + 2) 10. 5 – 3(c + 2) 11. x(4 x - 1) – 2 x(x + 1) 12. x(2 y-x) + y(x – 3 x)
Extension Problem
- Slides: 10