What is (x-1)^2-(y-3)^2 ?

The solution to (x-1)^2-(y-3)^2 is x^2-2x-y^2+6y-8

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simplify (x-1)^2-(y-3)^2

simplify

(x - 1)^{2} - (y - 3)^{2}

x^{2} - 2 x - y^{2} + 6 y - 8

Solution steps

(x - 1)^{2} - (y - 3)^{2}

Expand

(x - 1)^{2} : x^{2} - 2 x + 1

= x^{2} - 2 x + 1 - (y - 3)^{2}

Expand

- (y - 3)^{2} : - y^{2} + 6 y - 9

= x^{2} - 2 x + 1 - y^{2} + 6 y - 9

Group like terms

= x^{2} - 2 x - y^{2} + 6 y + 1 - 9

Subtract the numbers:

1 - 9 = - 8

= x^{2} - 2 x - y^{2} + 6 y - 8

\frac{1}{6} \div 10

\frac{5 ^{2}}{5 ^{- 3}}

\frac{x + 3}{x ^{2} - 25} - \frac{x - 1}{x - 5} + \frac{3}{x + 3}

- \frac{2}{3} - \frac{4}{7} + \frac{5}{3} + 3

\frac{lo g _{10} ( 4 )}{lo g _{10} ( 2 )}