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 (a^{2} + b^{2}). 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 (a^{2}) plus the product of 2, a and b (2ab) plus b square (b^{2}).

Therefore, the formula of (a+b)^{ 2} = a^{2} + 2 x a x b + b^{2}. 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)

= a^{2} + 2ab + b^{2}

Therefore, (a+b)^{ 2} = a^{2} + 2 x a x b + b^{2}

Form the above formula, we can get a^{2} + b^{2} = (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} = a^{2} + 2 x a x b + b^{2}

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

Therefore

(3x + 5y)^{ 2} = (3x)^{ 2} + 2 x 3x x 5y + (5y)^{ 2}

= 9x^{2} + 30xy + 25y^{2}

Therefore, (3x + 5y)^{ 2} = 9x^{2} + 30xy + 25y^{2}

Solve: (4a + 3) ^{2}

Solution:

According to the (a + b)^{ 2} formula,

(4a + 3)^{2} = (4a)^{ 2} + 2 x 4a x 3 + 3^{2}

= 16a^{2} + 24a + 9

Therefore, (4a + 3) ^{2 }= 16a^{2} + 24a + 9.

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