2007-02-19 23:07:03 · 7 answers · asked by klark kent 1 in Science & Mathematics ➔ Mathematics
Please also mention the formula for fractions numbers too
How to find the diffrence in CUBES of two positive whole numbers without calculating it?
2007-02-19 23:08:50 · update #1
difference in squares of 2 positive numbers
=a*2 - b*2
=(a+b) (a-b)
doesn't matter whether its whole numbers or fractions
difference in cubes of 2 positive numbers
=a*3 - b*3
=(a+b) (a*2 - ab + b*2)
I am not aware anything simpler than this.
2007-02-19 23:14:57 · answer #1 · answered by Anonymous · 1⤊ 0⤋
I assume you mean "without calculating the individual squares" as obviously however you get the answer, you will have calculated it one way or another.
suppose the two numbers are a and b and a^2 means a squared.
The phrase "difference of two squares" should be linked in your mind with the factorisation:
a^2 - b^2 = (a-b)(a+b) (which you can prove to yourself by multiplying out the brackets on the right hand side)
a and b can be any numbers, positive, negative and/or fractions.
Can't remember how to do difference of two cubes, but if you mess around with similar ideas you'll probably come up with something.
2007-02-20 07:19:21 · answer #2 · answered by lawomicron 4 · 0⤊ 0⤋
Easiest way to calculate the difference without actually finding the individual squares is just as everyone above have explained. Besides that you could also try by geometric method. Eg if you want 5^2-3^2. Construct square of dimensions 5. Construct another square of dimension 3. Place it on previously constructed square such that any two edges of smaller square coincides with those of larger. Area that's not covered by smaller square is your difference! Similar procedure could be applied to get difference in cubes. Construct cubes of dimensions 3 and 5 and continue...
2007-02-20 09:52:22 · answer #3 · answered by Mau 3 · 0⤊ 0⤋
Notice that a² - b² = (a+b)(a-b). So if you sum the two numbers, and multiply that by their difference, you get the difference in squares.
2007-02-20 07:18:20 · answer #4 · answered by Anonymous · 0⤊ 0⤋
a^2 - b^2 = (a+b)(a-b)
no need to calculate power of two
a^3 - b^3 = (a-b)[ (a-b)^2 + 3ab]
no need to calculate power of 3
2007-02-20 07:54:25 · answer #5 · answered by reza 2 · 0⤊ 0⤋
By drawing it on graph or 3-d.
2007-02-20 07:37:12 · answer #6 · answered by kalabalu 5 · 0⤊ 0⤋
add the numbers; substract the numbers and multiply them both.
2007-02-20 13:27:54 · answer #7 · answered by Narayanan Venkata S 1 · 0⤊ 0⤋