Solve (x-7)⋅(x 7)-(x-8)(x 8)

Question

Simplify the expression

- x^{2} + 15 x

Evaluate

(x - 7) (x \times 7) - (x - 8) (x \times 8)

Remove the parentheses

(x - 7) x \times 7 - (x - 8) x \times 8

Multiply the terms

More Steps

Multiply the terms

(x - 7) x \times 7

Use the commutative property to reorder the terms

(x - 7) \times 7 x

Multiply the terms

7 x (x - 7)

7 x (x - 7) - (x - 8) x \times 8

Multiply the terms

More Steps

Multiply the terms

(x - 8) x \times 8

Use the commutative property to reorder the terms

(x - 8) \times 8 x

Multiply the terms

8 x (x - 8)

7 x (x - 7) - 8 x (x - 8)

Expand the expression

More Steps

Calculate

7 x (x - 7)

Apply the distributive property

7 x \times x - 7 x \times 7

Multiply the terms

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

Multiply the numbers

7 x^{2} - 49 x

7 x^{2} - 49 x - 8 x (x - 8)

Expand the expression

More Steps

Calculate

- 8 x (x - 8)

Apply the distributive property

- 8 x \times x - (- 8 x \times 8)

Multiply the terms

- 8 x^{2} - (- 8 x \times 8)

Multiply the numbers

- 8 x^{2} - (- 64 x)

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

- 8 x^{2} + 64 x

7 x^{2} - 49 x - 8 x^{2} + 64 x

Subtract the terms

More Steps

Evaluate

7 x^{2} - 8 x^{2}

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

(7 - 8) x^{2}

Subtract the numbers

- x^{2}

- x^{2} - 49 x + 64 x

Solution

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Evaluate

- 49 x + 64 x

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

(- 49 + 64) x

Add the numbers

15 x

- x^{2} + 15 x

Show Solution

Factor the expression

(- x + 15) x

Evaluate

(x - 7) (x \times 7) - (x - 8) (x \times 8)

Remove the parentheses

(x - 7) x \times 7 - (x - 8) x \times 8

Use the commutative property to reorder the terms

(x - 7) \times 7 x - (x - 8) x \times 8

Multiply the terms

7 x (x - 7) - (x - 8) x \times 8

Use the commutative property to reorder the terms

7 x (x - 7) - (x - 8) \times 8 x

Multiply the terms

7 x (x - 7) - 8 x (x - 8)

Rewrite the expression

7 (x - 7) x - 8 (x - 8) x

Factor out x from the expression

(7 (x - 7) - 8 (x - 8)) x

Solution

(- x + 15) x

Show Solution

Find the roots

x_{1} = 0, x_{2} = 15

Evaluate

(x - 7) (x \times 7) - (x - 8) (x \times 8)

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

(x - 7) (x \times 7) - (x - 8) (x \times 8) = 0

Use the commutative property to reorder the terms

(x - 7) \times 7 x - (x - 8) (x \times 8) = 0

Use the commutative property to reorder the terms

(x - 7) \times 7 x - (x - 8) \times 8 x = 0

Multiply the terms

7 x (x - 7) - (x - 8) \times 8 x = 0

Multiply the terms

7 x (x - 7) - 8 x (x - 8) = 0

Calculate

More Steps

Evaluate

7 x (x - 7) - 8 x (x - 8)

Expand the expression

More Steps

Calculate

7 x (x - 7)

Apply the distributive property

7 x \times x - 7 x \times 7

Multiply the terms

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

Multiply the numbers

7 x^{2} - 49 x

7 x^{2} - 49 x - 8 x (x - 8)

Expand the expression

More Steps

Calculate

- 8 x (x - 8)

Apply the distributive property

- 8 x \times x - (- 8 x \times 8)

Multiply the terms

- 8 x^{2} - (- 8 x \times 8)

Multiply the numbers

- 8 x^{2} - (- 64 x)

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

- 8 x^{2} + 64 x

7 x^{2} - 49 x - 8 x^{2} + 64 x

Subtract the terms

More Steps

Evaluate

7 x^{2} - 8 x^{2}

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

(7 - 8) x^{2}

Subtract the numbers

- x^{2}

- x^{2} - 49 x + 64 x

Add the terms

More Steps

Evaluate

- 49 x + 64 x

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

(- 49 + 64) x

Add the numbers

15 x

- x^{2} + 15 x

- x^{2} + 15 x = 0

Factor the expression

More Steps

Evaluate

- x^{2} + 15 x

Rewrite the expression

- x \times x + x \times 15

Factor out - x from the expression

- x (x - 15)

- x (x - 15) = 0

When the product of factors equals 0,at least one factor is 0

- x = 0 x - 15 = 0

Solve the equation for x

x = 0 x - 15 = 0

Solve the equation for x

More Steps

Evaluate

x - 15 = 0

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

x = 0 + 15

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

x = 15

x = 0 x = 15

Solution

x_{1} = 0, x_{2} = 15

Show Solution