Solve (4r^3 3r^4)-(r^4-5r^3)

Question

Simplify the expression

12 r^{7} - r^{4} + 5 r^{3}

Evaluate

(4 r^{3} \times 3 r^{4}) - (r^{4} - 5 r^{3})

Multiply

More Steps

Multiply the terms

4 r^{3} \times 3 r^{4}

Multiply the terms

12 r^{3} \times r^{4}

Multiply the terms with the same base by adding their exponents

12 r^{3 + 4}

Add the numbers

12 r^{7}

12 r^{7} - (r^{4} - 5 r^{3})

Solution

12 r^{7} - r^{4} + 5 r^{3}

Show Solution

Factor the expression

r^{3} (12 r^{4} - r + 5)

Evaluate

(4 r^{3} \times 3 r^{4}) - (r^{4} - 5 r^{3})

Multiply

More Steps

Multiply the terms

4 r^{3} \times 3 r^{4}

Multiply the terms

12 r^{3} \times r^{4}

Multiply the terms with the same base by adding their exponents

12 r^{3 + 4}

Add the numbers

12 r^{7}

12 r^{7} - (r^{4} - 5 r^{3})

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

12 r^{7} - r^{4} + 5 r^{3}

Rewrite the expression

r^{3} \times 12 r^{4} - r^{3} \times r + r^{3} \times 5

Solution

r^{3} (12 r^{4} - r + 5)

Show Solution

Find the roots

r = 0

Evaluate

(4 r^{3} \times 3 r^{4}) - (r^{4} - 5 r^{3})

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

(4 r^{3} \times 3 r^{4}) - (r^{4} - 5 r^{3}) = 0

Multiply

More Steps

Multiply the terms

4 r^{3} \times 3 r^{4}

Multiply the terms

12 r^{3} \times r^{4}

Multiply the terms with the same base by adding their exponents

12 r^{3 + 4}

Add the numbers

12 r^{7}

12 r^{7} - (r^{4} - 5 r^{3}) = 0

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

12 r^{7} - r^{4} + 5 r^{3} = 0

Factor the expression

r^{3} (12 r^{4} - r + 5) = 0

Separate the equation into 2 possible cases

r^{3} = 0 12 r^{4} - r + 5 = 0

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

r = 0 12 r^{4} - r + 5 = 0

Solve the equation

r = 0 r \in / R

Solution

r = 0

Show Solution