Solve (x-4)^(2)⋅(3-2x)^(3)

Question

Simplify the expression

1035 x^{2} - 470 x^{3} + 100 x^{4} - 8 x^{5} - 1080 x + 432

Evaluate

(x - 4)^{2} (3 - 2 x)^{3}

Expand the expression

More Steps

(x^{2} - 8 x + 16) (3 - 2 x)^{3}

Expand the expression

More Steps

(x^{2} - 8 x + 16) (27 - 54 x + 36 x^{2} - 8 x^{3})

Apply the distributive property

x^{2} \times 27 - x^{2} \times 54 x + x^{2} \times 36 x^{2} - x^{2} \times 8 x^{3} - 8 x \times 27 - (- 8 x \times 54 x) - 8 x \times 36 x^{2} - (- 8 x \times 8 x^{3}) + 16 \times 27 - 16 \times 54 x + 16 \times 36 x^{2} - 16 \times 8 x^{3}

Use the commutative property to reorder the terms

27 x^{2} - x^{2} \times 54 x + x^{2} \times 36 x^{2} - x^{2} \times 8 x^{3} - 8 x \times 27 - (- 8 x \times 54 x) - 8 x \times 36 x^{2} - (- 8 x \times 8 x^{3}) + 16 \times 27 - 16 \times 54 x + 16 \times 36 x^{2} - 16 \times 8 x^{3}

Multiply the terms

More Steps

27 x^{2} - 54 x^{3} + x^{2} \times 36 x^{2} - x^{2} \times 8 x^{3} - 8 x \times 27 - (- 8 x \times 54 x) - 8 x \times 36 x^{2} - (- 8 x \times 8 x^{3}) + 16 \times 27 - 16 \times 54 x + 16 \times 36 x^{2} - 16 \times 8 x^{3}

Multiply the terms

More Steps

27 x^{2} - 54 x^{3} + 36 x^{4} - x^{2} \times 8 x^{3} - 8 x \times 27 - (- 8 x \times 54 x) - 8 x \times 36 x^{2} - (- 8 x \times 8 x^{3}) + 16 \times 27 - 16 \times 54 x + 16 \times 36 x^{2} - 16 \times 8 x^{3}

Multiply the terms

More Steps

27 x^{2} - 54 x^{3} + 36 x^{4} - 8 x^{5} - 8 x \times 27 - (- 8 x \times 54 x) - 8 x \times 36 x^{2} - (- 8 x \times 8 x^{3}) + 16 \times 27 - 16 \times 54 x + 16 \times 36 x^{2} - 16 \times 8 x^{3}

Multiply the numbers

27 x^{2} - 54 x^{3} + 36 x^{4} - 8 x^{5} - 216 x - (- 8 x \times 54 x) - 8 x \times 36 x^{2} - (- 8 x \times 8 x^{3}) + 16 \times 27 - 16 \times 54 x + 16 \times 36 x^{2} - 16 \times 8 x^{3}

Multiply the terms

More Steps

27 x^{2} - 54 x^{3} + 36 x^{4} - 8 x^{5} - 216 x - (- 432 x^{2}) - 8 x \times 36 x^{2} - (- 8 x \times 8 x^{3}) + 16 \times 27 - 16 \times 54 x + 16 \times 36 x^{2} - 16 \times 8 x^{3}

Multiply the terms

More Steps

27 x^{2} - 54 x^{3} + 36 x^{4} - 8 x^{5} - 216 x - (- 432 x^{2}) - 288 x^{3} - (- 8 x \times 8 x^{3}) + 16 \times 27 - 16 \times 54 x + 16 \times 36 x^{2} - 16 \times 8 x^{3}

Multiply the terms

More Steps

27 x^{2} - 54 x^{3} + 36 x^{4} - 8 x^{5} - 216 x - (- 432 x^{2}) - 288 x^{3} - (- 64 x^{4}) + 16 \times 27 - 16 \times 54 x + 16 \times 36 x^{2} - 16 \times 8 x^{3}

Multiply the numbers

27 x^{2} - 54 x^{3} + 36 x^{4} - 8 x^{5} - 216 x - (- 432 x^{2}) - 288 x^{3} - (- 64 x^{4}) + 432 - 16 \times 54 x + 16 \times 36 x^{2} - 16 \times 8 x^{3}

Multiply the numbers

27 x^{2} - 54 x^{3} + 36 x^{4} - 8 x^{5} - 216 x - (- 432 x^{2}) - 288 x^{3} - (- 64 x^{4}) + 432 - 864 x + 16 \times 36 x^{2} - 16 \times 8 x^{3}

Multiply the numbers

27 x^{2} - 54 x^{3} + 36 x^{4} - 8 x^{5} - 216 x - (- 432 x^{2}) - 288 x^{3} - (- 64 x^{4}) + 432 - 864 x + 576 x^{2} - 16 \times 8 x^{3}

Multiply the numbers

27 x^{2} - 54 x^{3} + 36 x^{4} - 8 x^{5} - 216 x - (- 432 x^{2}) - 288 x^{3} - (- 64 x^{4}) + 432 - 864 x + 576 x^{2} - 128 x^{3}

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

27 x^{2} - 54 x^{3} + 36 x^{4} - 8 x^{5} - 216 x + 432 x^{2} - 288 x^{3} + 64 x^{4} + 432 - 864 x + 576 x^{2} - 128 x^{3}

Add the terms

More Steps

1035 x^{2} - 54 x^{3} + 36 x^{4} - 8 x^{5} - 216 x - 288 x^{3} + 64 x^{4} + 432 - 864 x - 128 x^{3}

Subtract the terms

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1035 x^{2} - 470 x^{3} + 36 x^{4} - 8 x^{5} - 216 x + 64 x^{4} + 432 - 864 x

Add the terms

More Steps

1035 x^{2} - 470 x^{3} + 100 x^{4} - 8 x^{5} - 216 x + 432 - 864 x

Solution

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1035 x^{2} - 470 x^{3} + 100 x^{4} - 8 x^{5} - 1080 x + 432

Show Solution

Find the roots

x_{1} = \frac{3}{2}, x_{2} = 4

Alternative Form

x_{1} = 1.5, x_{2} = 4

Show Solution