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8 results for “perfect”

Formulae (6)

a^2 - b^2 = (a+b)(a-b)

Factors the difference of two perfect squares.

(a \pm b)^2 = a^2 \pm 2ab + b^2

Expands the square of a binomial.

x^2 + bx = \left(x+\frac{b}{2}\right)^2 - \frac{b^2}{4}

Rewrite a quadratic as a perfect square plus a constant.

N = 2^{p-1}(2^p - 1)

Euclid-Euler form of even perfect numbers.

S_n = n^2

The nth perfect square.

N = 2^{h+1} - 1

Total nodes in a perfect binary tree of height h.

The sum of the first n odd numbers is always a perfect square, exactly n².

Bracket the number between two perfect squares, then refine with a quick average step.