Solve (8x^3 - 2x^2 - 7) (4x^3 - 8x - 2)

Question

Simplify the expression

32 x^{6} - 64 x^{4} - 28 x^{3} - 8 x^{5} + 4 x^{2} + 56 x + 14

Evaluate

(8 x^{3} - 2 x^{2} - 7) (4 x^{3} - 8 x - 2)

Apply the distributive property

8 x^{3} \times 4 x^{3} - 8 x^{3} \times 8 x - 8 x^{3} \times 2 - 2 x^{2} \times 4 x^{3} - (- 2 x^{2} \times 8 x) - (- 2 x^{2} \times 2) - 7 \times 4 x^{3} - (- 7 \times 8 x) - (- 7 \times 2)

Multiply the terms

More Steps

32 x^{6} - 8 x^{3} \times 8 x - 8 x^{3} \times 2 - 2 x^{2} \times 4 x^{3} - (- 2 x^{2} \times 8 x) - (- 2 x^{2} \times 2) - 7 \times 4 x^{3} - (- 7 \times 8 x) - (- 7 \times 2)

Multiply the terms

More Steps

32 x^{6} - 64 x^{4} - 8 x^{3} \times 2 - 2 x^{2} \times 4 x^{3} - (- 2 x^{2} \times 8 x) - (- 2 x^{2} \times 2) - 7 \times 4 x^{3} - (- 7 \times 8 x) - (- 7 \times 2)

Multiply the numbers

32 x^{6} - 64 x^{4} - 16 x^{3} - 2 x^{2} \times 4 x^{3} - (- 2 x^{2} \times 8 x) - (- 2 x^{2} \times 2) - 7 \times 4 x^{3} - (- 7 \times 8 x) - (- 7 \times 2)

Multiply the terms

More Steps

32 x^{6} - 64 x^{4} - 16 x^{3} - 8 x^{5} - (- 2 x^{2} \times 8 x) - (- 2 x^{2} \times 2) - 7 \times 4 x^{3} - (- 7 \times 8 x) - (- 7 \times 2)

Multiply the terms

More Steps

32 x^{6} - 64 x^{4} - 16 x^{3} - 8 x^{5} - (- 16 x^{3}) - (- 2 x^{2} \times 2) - 7 \times 4 x^{3} - (- 7 \times 8 x) - (- 7 \times 2)

Multiply the numbers

32 x^{6} - 64 x^{4} - 16 x^{3} - 8 x^{5} - (- 16 x^{3}) - (- 4 x^{2}) - 7 \times 4 x^{3} - (- 7 \times 8 x) - (- 7 \times 2)

Multiply the numbers

32 x^{6} - 64 x^{4} - 16 x^{3} - 8 x^{5} - (- 16 x^{3}) - (- 4 x^{2}) - 28 x^{3} - (- 7 \times 8 x) - (- 7 \times 2)

Multiply the numbers

32 x^{6} - 64 x^{4} - 16 x^{3} - 8 x^{5} - (- 16 x^{3}) - (- 4 x^{2}) - 28 x^{3} - (- 56 x) - (- 7 \times 2)

Multiply the numbers

32 x^{6} - 64 x^{4} - 16 x^{3} - 8 x^{5} - (- 16 x^{3}) - (- 4 x^{2}) - 28 x^{3} - (- 56 x) - (- 14)

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

32 x^{6} - 64 x^{4} - 16 x^{3} - 8 x^{5} + 16 x^{3} + 4 x^{2} - 28 x^{3} + 56 x + 14

Solution

More Steps

32 x^{6} - 64 x^{4} - 28 x^{3} - 8 x^{5} + 4 x^{2} + 56 x + 14

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Factor the expression

2 (8 x^{3} - 2 x^{2} - 7) (2 x^{3} - 4 x - 1)

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Find the roots

x_{1} \approx - 1.267035, x_{2} \approx - 0.258652, x_{3} \approx 1.047478, x_{4} \approx 1.525687

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