Solve (2x-3)(x^6)-(x^6)

Question

Simplify the expression

2 x^{7} - 4 x^{6}

Evaluate

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

Multiply the terms

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

Expand the expression

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Calculate

x^{6} (2 x - 3)

Apply the distributive property

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

Multiply the terms

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Evaluate

x^{6} \times 2 x

Use the commutative property to reorder the terms

2 x^{6} \times x

Multiply the terms

2 x^{7}

2 x^{7} - x^{6} \times 3

Use the commutative property to reorder the terms

2 x^{7} - 3 x^{6}

2 x^{7} - 3 x^{6} - x^{6}

Solution

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Evaluate

- 3 x^{6} - x^{6}

Collect like terms by calculating the sum or difference of their coefficients

(- 3 - 1) x^{6}

Subtract the numbers

- 4 x^{6}

2 x^{7} - 4 x^{6}

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Factor the expression

2 x^{6} (x - 2)

Evaluate

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

Multiply the terms

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

Factor out x^{6} from the expression

x^{6} (2 x - 3 - 1)

Factor the expression

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Evaluate

2 x - 3 - 1

Subtract the numbers

2 x - 4

Factor the expression

2 (x - 2)

x^{6} \times 2 (x - 2)

Solution

2 x^{6} (x - 2)

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Find the roots

x_{1} = 0, x_{2} = 2

Evaluate

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

To find the roots of the expression,set the expression equal to 0

(2 x - 3) (x^{6}) - (x^{6}) = 0

Calculate

(2 x - 3) x^{6} - (x^{6}) = 0

Calculate

(2 x - 3) x^{6} - x^{6} = 0

Multiply the terms

x^{6} (2 x - 3) - x^{6} = 0

Calculate

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Evaluate

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

Expand the expression

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Calculate

x^{6} (2 x - 3)

Apply the distributive property

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

Multiply the terms

2 x^{7} - x^{6} \times 3

Use the commutative property to reorder the terms

2 x^{7} - 3 x^{6}

2 x^{7} - 3 x^{6} - x^{6}

Subtract the terms

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Evaluate

- 3 x^{6} - x^{6}

Collect like terms by calculating the sum or difference of their coefficients

(- 3 - 1) x^{6}

Subtract the numbers

- 4 x^{6}

2 x^{7} - 4 x^{6}

2 x^{7} - 4 x^{6} = 0

Factor the expression

2 x^{6} (x - 2) = 0

Divide both sides

x^{6} (x - 2) = 0

Separate the equation into 2 possible cases

x^{6} = 0 x - 2 = 0

The only way a power can be 0 is when the base equals 0

x = 0 x - 2 = 0

Solve the equation

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Evaluate

x - 2 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 2

Removing 0 doesn't change the value,so remove it from the expression

x = 2

x = 0 x = 2

Solution

x_{1} = 0, x_{2} = 2

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