E XPANSION - R EFLECTION Laura Delascasas 8C

I NTRODUCTION We learnt in class that we can use the expansion method instead of long multiplications in order to solve some algebraic expressions. For example (a + b)² can be solved using long multiplication : (a + b)² = (a + b) (a + b) = (a X a) + (a X b) + (b X a) + (b X b) = (a² + ab + ab + b²) = (a² + 2ab + b²) Or we can omit all the long multiplication and jump directly to the expanded form (a + b)² =(a² + 2ab + b²)

L EVEL 1-2 If I were an engineer 100 years ago, the expanded method may have been useful rather than just long multiplications because the method would help us to do our calculations faster and more efficiently, to be able to do our work faster and finish it in a limited amount of time. Otherwise if we use long multiplication it will take us longer to do the calculation, which will lead us to finishing the work in a longer amount of time. Also when you do long multiplication its must likely that you will have some mistakes during the operations.

L EVEL 3-4 Know lets consider Our method gets big and cumbersome when you have fractions, mixed numbers and decimals. (3 10/ /500)² = (3 10/30)² + 2((3 10/30)(390/500)) + (390/500)² = (3 10/30 x 3 10/30) + 2(3 10/30 x 390/500) + (390/500 x 390/500) Us you can see it’s becoming really big and cumbersome. But still it is more practical than the long multiplication.

L EVEL 5-6 Long multiplication is more efficient when you have whole numbers of one digit or two. (6+8)² = (6+8)(6+8) = = 196 Here it is with expanded form (6+8)² = 6² + 2(6x8) +8² = ((6x6) + 2x48 + (8x8) = = 196 As you can see it is more efficient solving it with long multiplication than Using expanded form. Let’s see it with long multiplication