Solve x*(2x-1)*(3-x) 2*(x-1)*(x^2*1) (a^3/2)^2 3/4

Evaluate

x (2 x - 1) (3 - x) \times 2 (x - 1) (x^{2} \times 1) (a^{3} \div 2)^{2} \times 3 \div 4

Remove the parentheses

x (2 x - 1) (3 - x) \times 2 (x - 1) x^{2} \times 1 \times (a^{3} \div 2)^{2} \times 3 \div 4

Rewrite the expression

x (2 x - 1) (3 - x) \times 2 (x - 1) x^{2} \times 1 \times (\frac{a ^{3}}{2})^{2} \times 3 \div 4

Multiply the terms

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\frac{3 x ^{3} a ^{6} ( 2 x - 1 ) ( 3 - x ) ( x - 1 )}{2} \div 4

Multiply by the reciprocal

\frac{3 x ^{3} a ^{6} ( 2 x - 1 ) ( 3 - x ) ( x - 1 )}{2} \times \frac{1}{4}

Multiply the terms

\frac{3 x ^{3} a ^{6} ( 2 x - 1 ) ( 3 - x ) ( x - 1 )}{2 \times 4}

Multiply the terms

\frac{3 x ^{3} a ^{6} ( 2 x - 1 ) ( 3 - x ) ( x - 1 )}{8}

Solution

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Evaluate

3 x^{3} a^{6} (2 x - 1) (3 - x) (x - 1)

Multiply the terms

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(6 x^{4} a^{6} - 3 x^{3} a^{6}) (3 - x) (x - 1)

Multiply the terms

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(21 x^{4} a^{6} - 6 x^{5} a^{6} - 9 x^{3} a^{6}) (x - 1)

Apply the distributive property

21 x^{4} a^{6} x - 21 x^{4} a^{6} \times 1 - 6 x^{5} a^{6} x - (- 6 x^{5} a^{6} \times 1) - 9 x^{3} a^{6} x - (- 9 x^{3} a^{6} \times 1)

Multiply the terms

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21 x^{5} a^{6} - 21 x^{4} a^{6} \times 1 - 6 x^{5} a^{6} x - (- 6 x^{5} a^{6} \times 1) - 9 x^{3} a^{6} x - (- 9 x^{3} a^{6} \times 1)

Any expression multiplied by 1 remains the same

21 x^{5} a^{6} - 21 x^{4} a^{6} - 6 x^{5} a^{6} x - (- 6 x^{5} a^{6} \times 1) - 9 x^{3} a^{6} x - (- 9 x^{3} a^{6} \times 1)

Multiply the terms

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21 x^{5} a^{6} - 21 x^{4} a^{6} - 6 x^{6} a^{6} - (- 6 x^{5} a^{6} \times 1) - 9 x^{3} a^{6} x - (- 9 x^{3} a^{6} \times 1)

Any expression multiplied by 1 remains the same

21 x^{5} a^{6} - 21 x^{4} a^{6} - 6 x^{6} a^{6} - (- 6 x^{5} a^{6}) - 9 x^{3} a^{6} x - (- 9 x^{3} a^{6} \times 1)

Multiply the terms

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21 x^{5} a^{6} - 21 x^{4} a^{6} - 6 x^{6} a^{6} - (- 6 x^{5} a^{6}) - 9 x^{4} a^{6} - (- 9 x^{3} a^{6} \times 1)

Any expression multiplied by 1 remains the same

21 x^{5} a^{6} - 21 x^{4} a^{6} - 6 x^{6} a^{6} - (- 6 x^{5} a^{6}) - 9 x^{4} a^{6} - (- 9 x^{3} a^{6})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

21 x^{5} a^{6} - 21 x^{4} a^{6} - 6 x^{6} a^{6} + 6 x^{5} a^{6} - 9 x^{4} a^{6} + 9 x^{3} a^{6}

Add the terms

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27 x^{5} a^{6} - 21 x^{4} a^{6} - 6 x^{6} a^{6} - 9 x^{4} a^{6} + 9 x^{3} a^{6}

Subtract the terms

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27 x^{5} a^{6} - 30 x^{4} a^{6} - 6 x^{6} a^{6} + 9 x^{3} a^{6}

\frac{27 x ^{5} a ^{6} - 30 x ^{4} a ^{6} - 6 x ^{6} a ^{6} + 9 x ^{3} a ^{6}}{8}

Simplify the expression