Solve 12a 8a^2 - 4a - 16a^2

Question

Simplify the expression

96 a^{3} - 4 a - 16 a^{2}

Evaluate

12 a \times 8 a^{2} - 4 a - 16 a^{2}

Solution

More Steps

Evaluate

12 a \times 8 a^{2}

Multiply the terms

96 a \times a^{2}

Multiply the terms with the same base by adding their exponents

96 a^{1 + 2}

Add the numbers

96 a^{3}

96 a^{3} - 4 a - 16 a^{2}

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Factor the expression

4 a (24 a^{2} - 1 - 4 a)

Evaluate

12 a \times 8 a^{2} - 4 a - 16 a^{2}

Multiply

More Steps

Evaluate

12 a \times 8 a^{2}

Multiply the terms

96 a \times a^{2}

Multiply the terms with the same base by adding their exponents

96 a^{1 + 2}

Add the numbers

96 a^{3}

96 a^{3} - 4 a - 16 a^{2}

Rewrite the expression

4 a \times 24 a^{2} - 4 a - 4 a \times 4 a

Solution

4 a (24 a^{2} - 1 - 4 a)

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Find the roots

a_{1} = \frac{1 - 7}{12}, a_{2} = 0, a_{3} = \frac{1 + 7}{12}

Alternative Form

a_{1} \approx - 0.137146, a_{2} = 0, a_{3} \approx 0.303813

Evaluate

12 a \times 8 a^{2} - 4 a - 16 a^{2}

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

12 a \times 8 a^{2} - 4 a - 16 a^{2} = 0

Multiply

More Steps

Multiply the terms

12 a \times 8 a^{2}

Multiply the terms

96 a \times a^{2}

Multiply the terms with the same base by adding their exponents

96 a^{1 + 2}

Add the numbers

96 a^{3}

96 a^{3} - 4 a - 16 a^{2} = 0

Factor the expression

4 a (24 a^{2} - 1 - 4 a) = 0

Divide both sides

a (24 a^{2} - 1 - 4 a) = 0

Separate the equation into 2 possible cases

a = 0 24 a^{2} - 1 - 4 a = 0

Solve the equation

More Steps

Evaluate

24 a^{2} - 1 - 4 a = 0

Rewrite in standard form

24 a^{2} - 4 a - 1 = 0

Substitute a= 24,b= - 4 and c= - 1 into the quadratic formula a = \frac{- b \pm b ^{2} - 4 a c}{2 a}

a = \frac{4 \pm ( - 4 ) ^{2} - 4 \times 24 ( - 1 )}{2 \times 24}

Simplify the expression

a = \frac{4 \pm ( - 4 ) ^{2} - 4 \times 24 ( - 1 )}{48}

Simplify the expression

More Steps

Evaluate

(- 4)^{2} - 4 \times 24 (- 1)

Multiply

(- 4)^{2} - (- 96)

Rewrite the expression

4^{2} - (- 96)

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

4^{2} + 96

Evaluate the power

16 + 96

Add the numbers

112

a = \frac{4 \pm 112}{48}

Simplify the radical expression

More Steps

Evaluate

112

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

16 \times 7

Write the number in exponential form with the base of 4

4^{2} \times 7

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

4^{2} \times 7

Reduce the index of the radical and exponent with 2

47

a = \frac{4 \pm 4 7}{48}

Separate the equation into 2 possible cases

a = \frac{4 + 4 7}{48} a = \frac{4 - 4 7}{48}

Simplify the expression

a = \frac{1 + 7}{12} a = \frac{4 - 4 7}{48}

Simplify the expression

a = \frac{1 + 7}{12} a = \frac{1 - 7}{12}

a = 0 a = \frac{1 + 7}{12} a = \frac{1 - 7}{12}

Solution

a_{1} = \frac{1 - 7}{12}, a_{2} = 0, a_{3} = \frac{1 + 7}{12}

Alternative Form

a_{1} \approx - 0.137146, a_{2} = 0, a_{3} \approx 0.303813

Show Solution