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

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

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

simplify

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

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

Solution steps

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Multiply the numbers:

2 \cdot 2 = 4

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

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

(x - 2) (x - 4)

\frac{x ^{2} - 4 x + 3}{( x - 2 ) ^{2}}

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

cos (x) d x + (1 + \frac{2}{y}) sin (x) d y

\frac{x ^{3}}{( x - 1 ) ( x + 2 ) ^{3} ( x ^{2} + 3 ) ^{2}}