What is (x+1/2)(y+1/2) ?

The solution to (x+1/2)(y+1/2) is ((2x+1)(2y+1))/4

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simplify (x+1/2)(y+1/2)

simplify

(x + \frac{1}{2}) (y + \frac{1}{2})

\frac{( 2 x + 1 ) ( 2 y + 1 )}{4}

Solution steps

(x + \frac{1}{2}) (y + \frac{1}{2})

Simplify

x + \frac{1}{2} : \frac{2 x + 1}{2}

= \frac{2 x + 1}{2} (y + \frac{1}{2})

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( 2 x + 1 ) ( y + \frac{1}{2} )}{2}

Simplify

(2 x + 1) (y + \frac{1}{2}) : \frac{( 2 x + 1 ) ( y \cdot 2 + 1 )}{2}

= \frac{\frac{( 2 x + 1 ) ( y \cdot 2 + 1 )}{2}}{2}

Apply the fraction rule:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{( 2 x + 1 ) ( y \cdot 2 + 1 )}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{( 2 x + 1 ) ( y \cdot 2 + 1 )}{4}

= \frac{( 2 x + 1 ) ( 2 y + 1 )}{4}

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