Question

Prove the identity(a+b) square=a square+2ab+b square

Answer 1

Simple
To prove (a+b)² = a²+b² + 2ab
(a+b)(a+b)
a(a+b)+b(a+b)
a²+ab+ab+b²
a²+b²+2ab
Therefore (a+b)² =a²+b²+2ab
Hence Proved

Answer 2

Concept

To determine the square of a binomial, use the (a + b)² formula. Additionally, several unique varieties of trinomials can be factored using this formula. An algebraic identity is contained in this formula. The formula for the square of a sum of two terms is (a + b)². A common method for factoring the binomial is the (a + b)² formula.

Given

Identity to be proved: (a ₊ b)² = a² ₊ 2ab ₊ b²

Find

We are required to validate the provided identification.

Solution

To determine the square of the product of two numbers, apply the algebraic identity (a ₊ b)². In order to determine the binomial's formula, take the form (a ₊ b)².

first all we have to do is multiply (a + b) by itself.

i.e, (a ₊ b)×(a ₊ b)

The product of two identical binomials can be expressed exponentially, according to exponentiation.

⇒ (a ₊ b)×(a ₊ b) = (a ₊ b)²

As a result, the two same sum basis binomials' product is frequently referred to as the special binomial product or the special product of binomials.

⇒  (a ₊ b)² = (a ₊ b)×(a ₊ b)

By multiplying the algebraic equation (a + b) with the same binomial, the (a + b)2 denotes the square of the sum of two terms. Consequently, use algebraic expression multiplication to multiple the algebraic expressions.

(a ₊ b)² = (a ₊ b)×(a ₊ b)

(a ₊ b)² = a × (a ₊ b) ₊ b × (a ₊ b)

(a ₊ b)² = (a × a) ₊ (a × b) ₊ (b × a) ₊ (b × b)  

(a ₊ b)² = a² ₊ ab ₊ ba ₊ b²

The expanded algebraic expression for the square of the sum of terms a and b is a²₊ab₊ba₊b². The commutative property states that the result of a and b is identical to the result of b and a. Therefore ab = ba.

(a ₊ b)² = a² ₊ ab ₊ ab ₊ b²

Now add the like terms in the expression

(a ₊ b)² = a² ₊ 2ab ₊ b²

Hence, we prove the identity (a ₊ b)² = a² ₊ 2ab ₊ b²

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