Solve 4p^2 12p-9 - ScanMath

Question

Simplify the expression

48 p^{3} - 9

Evaluate

4 p^{2} \times 12 p - 9

Solution

More Steps

Evaluate

4 p^{2} \times 12 p

Multiply the terms

48 p^{2} \times p

Multiply the terms with the same base by adding their exponents

48 p^{2 + 1}

Add the numbers

48 p^{3}

48 p^{3} - 9

Show Solution

Factor the expression

3 (16 p^{3} - 3)

Evaluate

4 p^{2} \times 12 p - 9

Multiply

More Steps

Evaluate

4 p^{2} \times 12 p

Multiply the terms

48 p^{2} \times p

Multiply the terms with the same base by adding their exponents

48 p^{2 + 1}

Add the numbers

48 p^{3}

48 p^{3} - 9

Solution

3 (16 p^{3} - 3)

Show Solution

Find the roots

p = \frac{3 12}{4}

Alternative Form

p \approx 0.572357

Evaluate

4 p^{2} \times 12 p - 9

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

4 p^{2} \times 12 p - 9 = 0

Multiply

More Steps

Multiply the terms

4 p^{2} \times 12 p

Multiply the terms

48 p^{2} \times p

Multiply the terms with the same base by adding their exponents

48 p^{2 + 1}

Add the numbers

48 p^{3}

48 p^{3} - 9 = 0

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

48 p^{3} = 0 + 9

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

48 p^{3} = 9

Divide both sides

\frac{48 p ^{3}}{48} = \frac{9}{48}

Divide the numbers

p^{3} = \frac{9}{48}

Cancel out the common factor 3

p^{3} = \frac{3}{16}

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

3 p^{3} = 3 \frac{3}{16}

Calculate

p = 3 \frac{3}{16}

Solution

More Steps

Evaluate

3 \frac{3}{16}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 3}{3 16}

Simplify the radical expression

More Steps

Evaluate

316

Write the expression as a product where the root of one of the factors can be evaluated

3 8 \times 2

Write the number in exponential form with the base of 2

3 2^{3} \times 2

The root of a product is equal to the product of the roots of each factor

3 2^{3} \times 32

Reduce the index of the radical and exponent with 3

232

\frac{3 3}{2 3 2}

Multiply by the Conjugate

\frac{3 3 \times 3 2 ^{2}}{2 3 2 \times 3 2 ^{2}}

Simplify

\frac{3 3 \times 3 4}{2 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

33 \times 34

The product of roots with the same index is equal to the root of the product

3 3 \times 4

Calculate the product

312

\frac{3 12}{2 3 2 \times 3 2 ^{2}}

Multiply the numbers

More Steps

Evaluate

232 \times 3 2^{2}

Multiply the terms

2 \times 2

Multiply the numbers

4

\frac{3 12}{4}

p = \frac{3 12}{4}

Alternative Form

p \approx 0.572357

Show Solution