Solve (2r - 3)(r^2 7r 9)

Question

Simplify the expression

126 r^{4} - 189 r^{3}

Evaluate

(2 r - 3) (r^{2} \times 7 r \times 9)

Remove the parentheses

(2 r - 3) r^{2} \times 7 r \times 9

Multiply the terms with the same base by adding their exponents

(2 r - 3) r^{2 + 1} \times 7 \times 9

Add the numbers

(2 r - 3) r^{3} \times 7 \times 9

Multiply the terms

(2 r - 3) r^{3} \times 63

Use the commutative property to reorder the terms

(2 r - 3) \times 63 r^{3}

Multiply the terms

63 r^{3} (2 r - 3)

Apply the distributive property

63 r^{3} \times 2 r - 63 r^{3} \times 3

Multiply the terms

More Steps

Evaluate

63 r^{3} \times 2 r

Multiply the numbers

126 r^{3} \times r

Multiply the terms

More Steps

Evaluate

r^{3} \times r

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

r^{3 + 1}

Add the numbers

r^{4}

126 r^{4}

126 r^{4} - 63 r^{3} \times 3

Solution

126 r^{4} - 189 r^{3}

Show Solution

r_{1} = 0, r_{2} = \frac{3}{2}

Alternative Form

r_{1} = 0, r_{2} = 1.5

Evaluate

(2 r - 3) (r^{2} \times 7 r \times 9)

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

(2 r - 3) (r^{2} \times 7 r \times 9) = 0

Multiply

More Steps

Multiply the terms

r^{2} \times 7 r \times 9

Multiply the terms with the same base by adding their exponents

r^{2 + 1} \times 7 \times 9

Add the numbers

r^{3} \times 7 \times 9

Multiply the terms

r^{3} \times 63

Use the commutative property to reorder the terms

63 r^{3}

(2 r - 3) \times 63 r^{3} = 0

Multiply the terms

63 r^{3} (2 r - 3) = 0

Elimination the left coefficient

r^{3} (2 r - 3) = 0

Separate the equation into 2 possible cases

r^{3} = 0 2 r - 3 = 0

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

r = 0 2 r - 3 = 0

Solve the equation

More Steps

Evaluate

2 r - 3 = 0

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

2 r = 0 + 3

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

2 r = 3

Divide both sides

\frac{2 r}{2} = \frac{3}{2}

Divide the numbers

r = \frac{3}{2}

r = 0 r = \frac{3}{2}

Solution

r_{1} = 0, r_{2} = \frac{3}{2}

Alternative Form

r_{1} = 0, r_{2} = 1.5

Show Solution