# a plus b whole square formula explained

Learn and know the formula of a plus b whole square in algebra. This is the first formula that we are going to learn in algebra chapter.

If we learn this formula, we can easily get the formula for a minus b whole square. Still one more formula also we can get i.e. a square plus b square (a2 + b2). So now we will learn what is a plus b whole square formula along with that we will also learn the proof for this formula.

## a plus b whole square formula as follows:

a plus b whole square mathematically written as (a+b)2. a plus b whole square (a+b)2 is equal to the a square (a2) plus the product of 2, a and b (2ab) plus b square (b2).

Therefore, the formula of (a+b) 2 = a2 + 2 x a x b + b2. This is one of the identities in algebra.

### Derivation (proof) of a plus b whole square formula:

Along with knowing the formula of a plus b whole square, we should also know how we got that formula i.e. proof.

We know that we can write, (a+b) 2   = (a+b) x (a+b)

= a x a + a x b + b x a + b x b (use multiplication of binomial with another binomial concept)

= a2 + 2ab + b2

Therefore, (a+b) 2 = a2 + 2 x a x b + b2

Form the above formula, we can get a2 + b2 = (a+b) 2 – 2 x a x b.

Note:

On this formula we can do one mathematics project also.

Examples:

Solve (3x + 5y) 2

Solution:

We know that the given problem is looking like a plus b whole square formula.

So   (a+b) 2 = a2 + 2 x a x b + b2

In this problem, we know that a = 3x and b = 5y

Therefore

(3x + 5y) 2     =    (3x) 2 + 2 x 3x x 5y + (5y) 2

=     9x2 + 30xy + 25y2

Therefore, (3x + 5y) 2     =     9x2 + 30xy + 25y2

Solve: (4a + 3) 2

Solution:

According to the (a + b) 2 formula,

(4a + 3)2 = (4a) 2 + 2 x 4a x 3 + 32

= 16a2 + 24a + 9

Therefore, (4a + 3) 2 = 16a2 + 24a + 9.