Expansion of whole square of a+b

Formula

${(a + b)}^2 = a^2 + b^2 + 2ab$

The formula in algebraic form is read as, $a$ plus $b$ whole square is equal to $a$ squared plus $b$ squared plus $2ab$.

The expansion of whole square of $a+b$ is true for all the values and it is derived in algebraic form. Hence, the $a+b$ whole square rule is called as an algebraic identity in algebra.

The property is an example for the square of sum of two unlike terms or special product of two same sum basis binomials. It is actually used in mathematics to expand square of sum of any two terms in terms of its terms and vice-versa.

Proof

The expansion of square of $a$ plus $b$ can be derived in two different methods.

Use

${(p + 6)}^2$ is an example for the binomial in square form, which is formed by the sum of two terms $p$ and $6$. It can be easily expanded by using $a+b$ whole square formula.

Take $a = p$ and $b = 6$ and substitute in the expansion of whole square of $a+b$ rule.

${(p + 6)}^2 = {(p)}^2 + {(6)}^2 + 2 \times p \times 6$

$\implies {(p + 6)}^2 = p^2 + 36 + 12p$

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