Solve 4(x^(3)-8x^(2) 9)^(3)⋅(6x^(2)-16x)

Question

Simplify the expression

24 x^{11} - 5248 x^{10} + 387072 x^{9} - 9953280 x^{8} + 64 \times 7 2^{3} x^{7}

Evaluate

4 (x^{3} - 8 x^{2} \times 9)^{3} (6 x^{2} - 16 x)

Multiply the terms

4 (x^{3} - 72 x^{2})^{3} (6 x^{2} - 16 x)

Expand the expression

More Steps

4 (x^{9} - 216 x^{8} + 15552 x^{7} - 7 2^{3} x^{6}) (6 x^{2} - 16 x)

Multiply the terms

More Steps

(4 x^{9} - 864 x^{8} + 62208 x^{7} - 4 \times 7 2^{3} x^{6}) (6 x^{2} - 16 x)

Apply the distributive property

4 x^{9} \times 6 x^{2} - 4 x^{9} \times 16 x - 864 x^{8} \times 6 x^{2} - (- 864 x^{8} \times 16 x) + 62208 x^{7} \times 6 x^{2} - 62208 x^{7} \times 16 x - 4 \times 7 2^{3} x^{6} \times 6 x^{2} - (- 4 \times 7 2^{3} x^{6} \times 16 x)

Multiply the terms

More Steps

24 x^{11} - 4 x^{9} \times 16 x - 864 x^{8} \times 6 x^{2} - (- 864 x^{8} \times 16 x) + 62208 x^{7} \times 6 x^{2} - 62208 x^{7} \times 16 x - 4 \times 7 2^{3} x^{6} \times 6 x^{2} - (- 4 \times 7 2^{3} x^{6} \times 16 x)

Multiply the terms

More Steps

24 x^{11} - 64 x^{10} - 864 x^{8} \times 6 x^{2} - (- 864 x^{8} \times 16 x) + 62208 x^{7} \times 6 x^{2} - 62208 x^{7} \times 16 x - 4 \times 7 2^{3} x^{6} \times 6 x^{2} - (- 4 \times 7 2^{3} x^{6} \times 16 x)

Multiply the terms

More Steps

24 x^{11} - 64 x^{10} - 5184 x^{10} - (- 864 x^{8} \times 16 x) + 62208 x^{7} \times 6 x^{2} - 62208 x^{7} \times 16 x - 4 \times 7 2^{3} x^{6} \times 6 x^{2} - (- 4 \times 7 2^{3} x^{6} \times 16 x)

Multiply the terms

More Steps

24 x^{11} - 64 x^{10} - 5184 x^{10} - (- 13824 x^{9}) + 62208 x^{7} \times 6 x^{2} - 62208 x^{7} \times 16 x - 4 \times 7 2^{3} x^{6} \times 6 x^{2} - (- 4 \times 7 2^{3} x^{6} \times 16 x)

Multiply the terms

More Steps

24 x^{11} - 64 x^{10} - 5184 x^{10} - (- 13824 x^{9}) + 373248 x^{9} - 62208 x^{7} \times 16 x - 4 \times 7 2^{3} x^{6} \times 6 x^{2} - (- 4 \times 7 2^{3} x^{6} \times 16 x)

Multiply the terms

More Steps

24 x^{11} - 64 x^{10} - 5184 x^{10} - (- 13824 x^{9}) + 373248 x^{9} - 995328 x^{8} - 4 \times 7 2^{3} x^{6} \times 6 x^{2} - (- 4 \times 7 2^{3} x^{6} \times 16 x)

Multiply the terms

More Steps

24 x^{11} - 64 x^{10} - 5184 x^{10} - (- 13824 x^{9}) + 373248 x^{9} - 995328 x^{8} - 24 \times 7 2^{3} x^{8} - (- 4 \times 7 2^{3} x^{6} \times 16 x)

Multiply the terms

More Steps

24 x^{11} - 64 x^{10} - 5184 x^{10} - (- 13824 x^{9}) + 373248 x^{9} - 995328 x^{8} - 24 \times 7 2^{3} x^{8} - (- 64 \times 7 2^{3} x^{7})

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

24 x^{11} - 64 x^{10} - 5184 x^{10} + 13824 x^{9} + 373248 x^{9} - 995328 x^{8} - 24 \times 7 2^{3} x^{8} + 64 \times 7 2^{3} x^{7}

Subtract the terms

More Steps

24 x^{11} - 5248 x^{10} + 13824 x^{9} + 373248 x^{9} - 995328 x^{8} - 24 \times 7 2^{3} x^{8} + 64 \times 7 2^{3} x^{7}

Add the terms

More Steps

24 x^{11} - 5248 x^{10} + 387072 x^{9} - 995328 x^{8} - 24 \times 7 2^{3} x^{8} + 64 \times 7 2^{3} x^{7}

Solution

More Steps

24 x^{11} - 5248 x^{10} + 387072 x^{9} - 9953280 x^{8} + 64 \times 7 2^{3} x^{7}

Show Solution

Factor the expression

8 x^{7} (x - 72)^{3} (3 x - 8)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{8}{3}, x_{3} = 72

Alternative Form

x_{1} = 0, x_{2} = 2. \dot{6}, x_{3} = 72

Show Solution