Solve (1-x^2/2)(1-4/2x^2)(1-9/2x^2)

$$( 1 - \frac { x ^ { 2 } } { 2 } ) ( 1 - \frac { 4 } { 2 } x ^ { 2 } ) ( 1 - \frac { 9 } { 2 } x ^ { 2 } )$$

Evaluate

$$\frac{-18x^{6}+\left(7x^{2}-2\right)^{2}}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

$$\left(\frac{2}{2}-\frac{x^{2}}{2}\right)\left(1-\frac{4}{2}x^{2}\right)\left(1-\frac{9}{2}x^{2}\right)$$

Since \frac{2}{2} and \frac{x^{2}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-x^{2}}{2}\left(1-\frac{4}{2}x^{2}\right)\left(1-\frac{9}{2}x^{2}\right)$$

Divide 4 by 2 to get 2.

$$\frac{2-x^{2}}{2}\left(1-2x^{2}\right)\left(1-\frac{9}{2}x^{2}\right)$$

Express \frac{2-x^{2}}{2}\left(1-2x^{2}\right) as a single fraction.

$$\frac{\left(2-x^{2}\right)\left(1-2x^{2}\right)}{2}\left(1-\frac{9}{2}x^{2}\right)$$

Use the distributive property to multiply 2-x^{2} by 1-2x^{2} and combine like terms.

$$\frac{2-5x^{2}+2x^{4}}{2}\left(1-\frac{9}{2}x^{2}\right)$$

Use the distributive property to multiply \frac{2-5x^{2}+2x^{4}}{2} by 1-\frac{9}{2}x^{2}.

$$\frac{2-5x^{2}+2x^{4}}{2}-\frac{9}{2}\times \frac{2-5x^{2}+2x^{4}}{2}x^{2}$$

Multiply -\frac{9}{2} times \frac{2-5x^{2}+2x^{4}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2-5x^{2}+2x^{4}}{2}+\frac{-9\left(2-5x^{2}+2x^{4}\right)}{2\times 2}x^{2}$$

Express \frac{-9\left(2-5x^{2}+2x^{4}\right)}{2\times 2}x^{2} as a single fraction.

$$\frac{2-5x^{2}+2x^{4}}{2}+\frac{-9\left(2-5x^{2}+2x^{4}\right)x^{2}}{2\times 2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 2\times 2 is 2\times 2. Multiply \frac{2-5x^{2}+2x^{4}}{2} times \frac{2}{2}.

$$\frac{2\left(2-5x^{2}+2x^{4}\right)}{2\times 2}+\frac{-9\left(2-5x^{2}+2x^{4}\right)x^{2}}{2\times 2}$$

Since \frac{2\left(2-5x^{2}+2x^{4}\right)}{2\times 2} and \frac{-9\left(2-5x^{2}+2x^{4}\right)x^{2}}{2\times 2} have the same denominator, add them by adding their numerators.

$$\frac{2\left(2-5x^{2}+2x^{4}\right)-9\left(2-5x^{2}+2x^{4}\right)x^{2}}{2\times 2}$$

Do the multiplications in 2\left(2-5x^{2}+2x^{4}\right)-9\left(2-5x^{2}+2x^{4}\right)x^{2}.

$$\frac{4-10x^{2}+4x^{4}-18x^{2}+45x^{4}-18x^{6}}{2\times 2}$$

Combine like terms in 4-10x^{2}+4x^{4}-18x^{2}+45x^{4}-18x^{6}.

$$\frac{4-28x^{2}+49x^{4}-18x^{6}}{2\times 2}$$

Expand 2\times 2.

$$\frac{4-28x^{2}+49x^{4}-18x^{6}}{4}$$

Expand

$$-\frac{9x^{6}}{2}+\frac{49x^{4}}{4}-7x^{2}+1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

$$\left(\frac{2}{2}-\frac{x^{2}}{2}\right)\left(1-\frac{4}{2}x^{2}\right)\left(1-\frac{9}{2}x^{2}\right)$$

Since \frac{2}{2} and \frac{x^{2}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-x^{2}}{2}\left(1-\frac{4}{2}x^{2}\right)\left(1-\frac{9}{2}x^{2}\right)$$

Divide 4 by 2 to get 2.

$$\frac{2-x^{2}}{2}\left(1-2x^{2}\right)\left(1-\frac{9}{2}x^{2}\right)$$

Express \frac{2-x^{2}}{2}\left(1-2x^{2}\right) as a single fraction.

$$\frac{\left(2-x^{2}\right)\left(1-2x^{2}\right)}{2}\left(1-\frac{9}{2}x^{2}\right)$$

Use the distributive property to multiply 2-x^{2} by 1-2x^{2} and combine like terms.

$$\frac{2-5x^{2}+2x^{4}}{2}\left(1-\frac{9}{2}x^{2}\right)$$

Use the distributive property to multiply \frac{2-5x^{2}+2x^{4}}{2} by 1-\frac{9}{2}x^{2}.

$$\frac{2-5x^{2}+2x^{4}}{2}-\frac{9}{2}\times \frac{2-5x^{2}+2x^{4}}{2}x^{2}$$

Multiply -\frac{9}{2} times \frac{2-5x^{2}+2x^{4}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2-5x^{2}+2x^{4}}{2}+\frac{-9\left(2-5x^{2}+2x^{4}\right)}{2\times 2}x^{2}$$

Express \frac{-9\left(2-5x^{2}+2x^{4}\right)}{2\times 2}x^{2} as a single fraction.

$$\frac{2-5x^{2}+2x^{4}}{2}+\frac{-9\left(2-5x^{2}+2x^{4}\right)x^{2}}{2\times 2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 2\times 2 is 2\times 2. Multiply \frac{2-5x^{2}+2x^{4}}{2} times \frac{2}{2}.

$$\frac{2\left(2-5x^{2}+2x^{4}\right)}{2\times 2}+\frac{-9\left(2-5x^{2}+2x^{4}\right)x^{2}}{2\times 2}$$

Since \frac{2\left(2-5x^{2}+2x^{4}\right)}{2\times 2} and \frac{-9\left(2-5x^{2}+2x^{4}\right)x^{2}}{2\times 2} have the same denominator, add them by adding their numerators.

$$\frac{2\left(2-5x^{2}+2x^{4}\right)-9\left(2-5x^{2}+2x^{4}\right)x^{2}}{2\times 2}$$

Do the multiplications in 2\left(2-5x^{2}+2x^{4}\right)-9\left(2-5x^{2}+2x^{4}\right)x^{2}.

$$\frac{4-10x^{2}+4x^{4}-18x^{2}+45x^{4}-18x^{6}}{2\times 2}$$

Combine like terms in 4-10x^{2}+4x^{4}-18x^{2}+45x^{4}-18x^{6}.

$$\frac{4-28x^{2}+49x^{4}-18x^{6}}{2\times 2}$$

Expand 2\times 2.

$$\frac{4-28x^{2}+49x^{4}-18x^{6}}{4}$$