Let us visit some mathematical expressions typically produced due to distributive laws and regulations and rules and rules and rules of addition and multiplication. For that are used for this tutorial, let us restrict our domain to two digit figures.
(a b) squared = a squared b squared 2 * a *b.
(a-b) squared = a squared b squared – 2 * a * b.
(a b) * ( c d) = ac ad bc bd.
(a b) * ( c – d) = ac – ad bc – bd.
(a-b) *(c d) = ac ad -bc -bd.
(a-b)(c-d) = ac – ad – bc bd.
Let us rewrite several K like a sum or difference of two figures inside the form
(a b) or (a-b), where a is the same as the nearest multiple of 10 under or just greater than the quantity K.
For example 63 might be re-written as (60 3) and 68 might be re-written as
(70 – 2). 73 might be re-written as 70 3 and 79 might be re-written as 80 – 1.
Let us first calculate 47 * 47
Let us utilize the formula (a-b) * (a-b) = a * a – 2 * a * b b *b where a = 50 and b = 3.
So 47 * 47 = 2500 – 300 9 = 2209.
Let us make use of these formula (a b – – – -) * (a b) = a*a 2 * a * b b*b and calculate 73 * 73
73 * 73 = (70 3) ( 70 3 ) = 4900 420 9 = 5329.
26 * 26 = ( 30 – 4)(30 – 4) = 900 – 240 16 = 676.
Use (a b)(c d) to calculate 93 * 57 as
(90 3) * ( 50 7 ) = 4500 630 150 21, Simplify this
by scripting this as 4500 600 30 100 50 20 1, 4500 700 101 which can be easily calculated as 5301
Let us similarly calculate 47 * 69 while using the expression for (a-b) (c-d). Let us rewrite the merchandise as (50-3) (70-1). Expanding the individual terms as
3500 – 50 – 210 3, rewriting this as 3500 – 200 – 60 3 rewriting this as
3500 – 200 – 60 3 So 47 * 63 = 3243.
While using the expression (a-b)(c d) let us calculate 43 * 88, Rewrite the initial expression as (40 3)*(90 – 2). Compute individual sums as 3600 – 80 270 – 6 = 3870 – 86 = 3870 – 70 – 16 = 3800 – 16 = 3784.
Let us utilize the expression (a-b) (c-d) = ac – ad -bc bd to calculate 57 * 79 quickly. Rewriting this as (60 – 3) * (80 -1) = 4800 – 60 – 240 3 = 4800 – 300 3 = 4503.
Extending situation study to 3 digit figures, these simply sums of merchandise might be formulated using distributive laws and regulations and rules and rules and rules of addition and multiplication correspondingly.
Let us calculate 153 * 94 quickly, by rewriting 153 as 100 50 3 and 94 as 90 4. Let us write the initial product as (100 50 3) (90 4) the sum individual terms is 9000 400 4500 200 270 12. Sort is really by thousands, hundredths and Units place. 13000 1000 300 82 quickly calculate the sum as 14382.
