Solve (x-1)(x+2)(x+3)(x+6)

Question

Simplify the expression

Solution

x^{4} + 10 x^{3} + 25 x^{2} - 36

Evaluate

(x - 1) (x + 2) (x + 3) (x + 6)

Multiply the terms

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

Multiply the terms

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(x^{3} + 4 x^{2} + x - 6) (x + 6)

Apply the distributive property

x^{3} \times x + x^{3} \times 6 + 4 x^{2} \times x + 4 x^{2} \times 6 + x \times x + x \times 6 - 6 x - 6 \times 6

Multiply the terms

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x^{4} + x^{3} \times 6 + 4 x^{2} \times x + 4 x^{2} \times 6 + x \times x + x \times 6 - 6 x - 6 \times 6

Use the commutative property to reorder the terms

x^{4} + 6 x^{3} + 4 x^{2} \times x + 4 x^{2} \times 6 + x \times x + x \times 6 - 6 x - 6 \times 6

Multiply the terms

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x^{4} + 6 x^{3} + 4 x^{3} + 4 x^{2} \times 6 + x \times x + x \times 6 - 6 x - 6 \times 6

Multiply the numbers

x^{4} + 6 x^{3} + 4 x^{3} + 24 x^{2} + x \times x + x \times 6 - 6 x - 6 \times 6

Multiply the terms

x^{4} + 6 x^{3} + 4 x^{3} + 24 x^{2} + x^{2} + x \times 6 - 6 x - 6 \times 6

Use the commutative property to reorder the terms

x^{4} + 6 x^{3} + 4 x^{3} + 24 x^{2} + x^{2} + 6 x - 6 x - 6 \times 6

Multiply the numbers

x^{4} + 6 x^{3} + 4 x^{3} + 24 x^{2} + x^{2} + 6 x - 6 x - 36

Add the terms

More Steps

x^{4} + 10 x^{3} + 24 x^{2} + x^{2} + 6 x - 6 x - 36

Add the terms

More Steps

x^{4} + 10 x^{3} + 25 x^{2} + 6 x - 6 x - 36

The sum of two opposites equals 0

More Steps

x^{4} + 10 x^{3} + 25 x^{2} + 0 - 36

Solution

x^{4} + 10 x^{3} + 25 x^{2} - 36

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Find the roots of the algebra expression

x_{1} = - 6, x_{2} = - 3, x_{3} = - 2, x_{4} = 1

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