What is (m^2n^2-3/4)(m^2n^2+1/2) ?

The solution to (m^2n^2-3/4)(m^2n^2+1/2) is ((4m^2n^2-3)(2m^2n^2+1))/8

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simplify (m^2n^2-3/4)(m^2n^2+1/2)

simplify

(m^{2} n^{2} - \frac{3}{4}) (m^{2} n^{2} + \frac{1}{2})

\frac{( 4 m ^{2} n ^{2} - 3 ) ( 2 m ^{2} n ^{2} + 1 )}{8}

Solution steps

(m^{2} n^{2} - \frac{3}{4}) (m^{2} n^{2} + \frac{1}{2})

Simplify

m^{2} n^{2} - \frac{3}{4} : \frac{4 m ^{2} n ^{2} - 3}{4}

= \frac{4 m ^{2} n ^{2} - 3}{4} (m^{2} n^{2} + \frac{1}{2})

Apply the fraction rule:

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

= \frac{( 4 m ^{2} n ^{2} - 3 ) ( m ^{2} n ^{2} + \frac{1}{2} )}{4}

Simplify

(4 m^{2} n^{2} - 3) (m^{2} n^{2} + \frac{1}{2}) : \frac{( 4 m ^{2} n ^{2} - 3 ) ( m ^{2} n ^{2} \cdot 2 + 1 )}{2}

= \frac{\frac{( 4 m ^{2} n ^{2} - 3 ) ( m ^{2} n ^{2} \cdot 2 + 1 )}{2}}{4}

Apply the fraction rule:

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

= \frac{( 4 m ^{2} n ^{2} - 3 ) ( m ^{2} n ^{2} \cdot 2 + 1 )}{2 \cdot 4}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{( 4 m ^{2} n ^{2} - 3 ) ( m ^{2} n ^{2} \cdot 2 + 1 )}{8}

= \frac{( 4 m ^{2} n ^{2} - 3 ) ( 2 m ^{2} n ^{2} + 1 )}{8}

sin^{2} (θ) (1 + cot (θ))

\frac{1}{4 \cdot π \cdot 0.02} (\frac{1}{0.65} - \frac{1}{0.75}) + \frac{1}{5}

- \frac{5 ( x + 4 )}{7}

\frac{1}{12} (cos (8 t) - 5 sin (8 t))

What is (m^2n^2-3/4)(m^2n^2+1/2) ?
The solution to (m^2n^2-3/4)(m^2n^2+1/2) is ((4m^2n^2-3)(2m^2n^2+1))/8