Math Doubts

a-b whole square formula

Formula

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

It is called $a$ minus $b$ whole formula and the identity is used to expand the square of difference of two terms in terms of same terms and vice-versa.

Proof

The $a-b$ whole square formula can be derived in two different mathematical approaches.

Use

The a-b whole square identity is mainly used in mathematics to expand square of any binomial which is formed by the difference of two terms.

For example, $(3x-4y)^2$. It is in the form of $(a-b)^2$ formula. So, expand $(3x-4y)^2$, same as the expansion of $a-b$ whole square formula.

$(3x-4y)^2 = {(3x)}^2 + {(4y)}^2 -2(3x)(4y)$

$\implies (3x-4y)^2 = 9x^2 + 16y^2 -24xy$

You can get more examples in our worksheet of a-b whole square formula and enhance your knowledge.



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