সাইন আপ করুন
সাইন আপ করুন
লগিন করুন
রিসেট পাসওয়ার্ড
পাসওয়ার্ড ভুলে গেছেন? আপনার ইমেইল এড্রেস দিন। ইমেইলের মাধ্যমে আপনি নতুন পাসওয়ার্ড তৈরির লিংক পেয়ে যাবেন।
আপনি কেন মনে করছেন এই প্রশ্নটি রিপোর্ট করা উচিৎ?
আপনি কেন মনে করছেন এই উত্তরটি রিপোর্ট করা উচিৎ?
আপনি কেন মনে করছেন এই ব্যক্তিকে রিপোর্ট করা উচিৎ?
At first we need to understand (a + b)3 formula in detail in the following section. The (a + b)^3 Formula To find the cube of a binomial, we will just multiply (a + b)(a + b)(a + b). (a + b)3 formula is also an identity. It holds true for every value of a and b.The (a + b)3 is given as, (a + b)3 = (বিস্তারিত পড়ুন
At first we need to understand (a + b)3 formula in detail in the following section.
The (a + b)^3 Formula
To find the cube of a binomial, we will just multiply (a + b)(a + b)(a + b). (a + b)3 formula is also an identity. It holds true for every value of a and b.The (a + b)3 is given as,
(a + b)3 = (a + b)(a + b)(a + b)
= (a2 + 2ab + b2)(a + b)
= a3 + a2b + 2a2b + 2ab2 + ab2 + b3
= a3 + 3a2b + 3ab2 + b3
= a3 + 3ab(a+b) + b3
Therefore, (a + b)^3 formula is:
(a + b)3 = a3 + 3a2b + 3ab2 + b3
Examples (a + b)3 Formula
Example : Solve the following expression using suitable algebraic identity: (2x + 3y)3
Solution:
To find: (2x + 3y)3
Using (a + b)3 Formula,
(a + b)3 = a3 + 3a2b + 3ab2 + b3
= (2x)3 + 3 × (2x)2 × 3y + 3 × (2x) × (3y)2 + (3y)3
= 8x3 + 36x2y + 54xy2 + 27y3
Answer: (2x + 3y)3 = 8x3 + 36x2y + 54xy2 + 27y3
Example : Find the value of x3 + 8y3 if x + 2y = 6 and xy = 2.
Solution:
To find: x3 + 8y3
Given: x + 2y = 6
xy = 2
Using (a + b)3 formula,
(a + b)3 = a3 + 3a2b + 3ab2 + b3
Here, a = x; b = 2y
Therefore,
(x + 2y)3 = x3 + 3 × x2 × (2y) + 3 × x × (2y)2 + (2y)3
(x + 2y)3 = x3 + 6x2y + 12xy2 + 8y3
63 = x3 + 6xy(x + 2y) + 8y3
216 = x3 + 6 × 2 × 6 + 8y3
x3 + 8y3 = 144
Answer: x3 + 8y3 = 144
Example : Solve the following expression using (a + b)3 formula:
(5x + 2y)3
Solution:
To find: (5x + 2y)3
Using (a + b)3 Formula,
(a + b)3 = a3 + 3a2b + 3ab2 + b3
= (5x)3 + 3 × (5x)2 × 2y + 3 × (5x) × (2y)2 + (2y)3
= 125x3 + 150x2y + 60xy2 + 8y3
Answer: (5x + 2y)3 = 125x3 + 150x2y + 60xy2 + 8y3
Expansion of (a + b)3 Formula
(a + b)3 formula is read as a plus b whole cube. Its expansion is expressed as (a + b)3 = a3 + 3a2b + 3ab2 + b3
Simplify Numbers Using the (a + b)3 Formula
Let us understand the use of the (a + b)3 formula with the help of the following example.
Example: Find the value of (20 + 5)3 using the (a + b)3 formula.
To find: (20 + 5)3
Let us assume that a = 20 and b = 5.
We will substitute these in the formula of (a + b)3.
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(20+5)3 = 203 + 3(20)2(5) + 3(20)(5)2 + 53
=8000 + 6000 + 1500 + 125
= 15625
Answer: (20 + 5)3 = 15625.
Using the (a + b)3 Formula Steps
The following steps are followed while using (a + b)3 formula.
Thanks!