1. BINOMIALEXPANSION REFLECTION Ibrahim Almana 8D

2. Engineers were calculating the area of a square figure 100 years back by squaring the length of a side. If each side were measured by number 7, for example, then the area would be measured by 7 × 7 = 49.

3. Suppose you want to multiply 21x19. The quick way to do it using this formula is to write it as (20+1)(20-1). Then it is a sum and difference, so you can use the formula, and it is 202-12 Both of those computations are easy to do mentally. We compute 202 by computing 22 and adding two zeros, so that gives us 400, and since 12 is 1, the answer is 399. we can do this to good effect whenever we can write the numbers as the sum and difference of the same numbers and those numbers are easy to square.

4. The easy way to unsure that is to use numbers that are the same amount up and down from a multiple of 10, like 33x27, 55x45, or 62x58. For 33x27, you could see it as (30+3)(30-3), and that would mean you would just need to square 30 and square 3 and find the difference, which would be 900-9=891. With a little bit practice you can get quite quick at this. 55x45 and 62x58 are left as exercises for the student.

5. Look at a square figure in which each side is 28. Then the area of that square will be 28 × 28. But we can break up 28 into 20 + 8. Therefore the entire square will be composed of the following: Look at a square figure in which each side is 28. Then the area of that square will be 28 × 28. But we can break up 28 into 20 + 8. Therefore the entire square will be composed of the following:

6. The square of 20, which is 400. Two rectangles, each with area 20 × 8 = 160. And the square of 8, which is 64. In other words, the square of 20 + 8 is equal to The square of 20, plus Two times 20 × 8, plus The square of 8. 400 + 320 + 64 = 784. This is not a difficult mental calculation.

7. (a + b)² = (a + b)(a + b) = a² + 2ab + b² The square of any binomial produces the following three terms: 1. The square of the first term of the binomial: a² 2. Twice the product of the two terms: 2ab 3. The square of the second term: b²

8. Most cases if algebraic formulas were available but when the numbers are of decimals or fractions long multiplication will be more

9. When we multiply by long multiplication method It requires memorization of the multiplication table for single digits.

10. We use the binomial theorem to help us expand binomials to any given power without direct multiplication. As we have seen, multiplication can be time-consuming or even not possible in some cases.

11. The most commonly used ones. (A+B)(A-B)=A2-B2 (A+B)2=A2+2AB+B2 (A-B)2=A2-2AB+B2 They come up often enough that it is worth memorizing them, not just for multiplying, but for later things as well, like factoring and completing the square where it is helpful to be able to recognize forms like these. You derive these formulas by applying FOIL just once for each of the formulas and then you will never have to use FOIL for any expressions of their form. Instead you can just write down the answer by knowing the formula.

12. There are many chances that long multiplication is easier than calculating by using this binomial formula.