Solve 7t^28t-56 - ScanMath

Question

Simplify the expression

56 t^{3} - 56

Evaluate

7 t^{2} \times 8 t - 56

Solution

More Steps

Evaluate

7 t^{2} \times 8 t

Multiply the terms

56 t^{2} \times t

Multiply the terms with the same base by adding their exponents

56 t^{2 + 1}

Add the numbers

56 t^{3}

56 t^{3} - 56

Show Solution

56 (t - 1) (t^{2} + t + 1)

Evaluate

7 t^{2} \times 8 t - 56

Evaluate

More Steps

Evaluate

7 t^{2} \times 8 t

Multiply the terms

56 t^{2} \times t

Multiply the terms with the same base by adding their exponents

56 t^{2 + 1}

Add the numbers

56 t^{3}

56 t^{3} - 56

Factor out 56 from the expression

56 (t^{3} - 1)

Solution

More Steps

Evaluate

t^{3} - 1

Rewrite the expression in exponential form

t^{3} - 1^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(t - 1) (t^{2} + t \times 1 + 1^{2})

Any expression multiplied by 1 remains the same

(t - 1) (t^{2} + t + 1^{2})

1 raised to any power equals to 1

(t - 1) (t^{2} + t + 1)

56 (t - 1) (t^{2} + t + 1)

Show Solution

t = 1

Evaluate

7 t^{2} \times 8 t - 56

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

7 t^{2} \times 8 t - 56 = 0

Multiply

More Steps

Multiply the terms

7 t^{2} \times 8 t

Multiply the terms

56 t^{2} \times t

Multiply the terms with the same base by adding their exponents

56 t^{2 + 1}

Add the numbers

56 t^{3}

56 t^{3} - 56 = 0

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

56 t^{3} = 0 + 56

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

56 t^{3} = 56

Divide both sides

\frac{56 t ^{3}}{56} = \frac{56}{56}

Divide the numbers

t^{3} = \frac{56}{56}

Divide the numbers

More Steps

Evaluate

\frac{56}{56}

Reduce the numbers

\frac{1}{1}

Calculate

1

t^{3} = 1

Take the 3 -th root on both sides of the equation

3 t^{3} = 31

Calculate

t = 31

Solution

t = 1

Show Solution