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Popular >

expand ((3x)/2)(x-2)(-3x+6)(x^2-3x+1)

Solution

expand

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

Solution

- \frac{9 x ^{5}}{2} + \frac{63 x ^{4}}{2} - \frac{153 x ^{3}}{2} + 72 x^{2} - 18 x

Solution steps

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

Apply rule:

(a) = a

(\frac{3 x}{2}) = \frac{3 x}{2}

= \frac{3 x}{2} (x - 2) (- 3 x + 6) (x^{2} - 3 x + 1)

Apply FOIL method

(x - 2) (- 3 x + 6) : - 3 x^{2} + 12 x - 12

= \frac{3 x}{2} (- 3 x^{2} + 12 x - 12) (x^{2} - 3 x + 1)

Expand

(- 3 x^{2} + 12 x - 12) (x^{2} - 3 x + 1) : - 3 x^{4} + 21 x^{3} - 51 x^{2} + 48 x - 12

= \frac{3 x}{2} (- 3 x^{4} + 21 x^{3} - 51 x^{2} + 48 x - 12)

Distribute parentheses

= \frac{3 x}{2} (- 3 x^{4}) + \frac{3 x}{2} \cdot 21 x^{3} + \frac{3 x}{2} (- 51 x^{2}) + \frac{3 x}{2} \cdot 48 x + \frac{3 x}{2} (- 12)

Simplify

\frac{3 x}{2} (- 3 x^{4}) + \frac{3 x}{2} \cdot 21 x^{3} + \frac{3 x}{2} (- 51 x^{2}) + \frac{3 x}{2} \cdot 48 x + \frac{3 x}{2} (- 12) : - \frac{9 x ^{5}}{2} + \frac{63 x ^{4}}{2} - \frac{153 x ^{3}}{2} + 72 x^{2} - 18 x

= - \frac{9 x ^{5}}{2} + \frac{63 x ^{4}}{2} - \frac{153 x ^{3}}{2} + 72 x^{2} - 18 x

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Frequently Asked Questions (FAQ)

What is expand ((3x)/2)(x-2)(-3x+6)(x^2-3x+1) ?
The solution to expand ((3x)/2)(x-2)(-3x+6)(x^2-3x+1) is -(9x^5)/2+(63x^4)/2-(153x^3)/2+72x^2-18x

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