Solve (a-4)(a^4)a^24

Question

Simplify the expression

4 a^{7} - 16 a^{6}

Evaluate

(a - 4) a^{4} \times a^{2} \times 4

Multiply the terms with the same base by adding their exponents

(a - 4) a^{4 + 2} \times 4

Add the numbers

(a - 4) a^{6} \times 4

Use the commutative property to reorder the terms

(a - 4) \times 4 a^{6}

Multiply the terms

4 a^{6} (a - 4)

Apply the distributive property

4 a^{6} \times a - 4 a^{6} \times 4

Multiply the terms

More Steps

Evaluate

a^{6} \times a

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

a^{6 + 1}

Add the numbers

a^{7}

4 a^{7} - 4 a^{6} \times 4

Solution

4 a^{7} - 16 a^{6}

Show Solution

a_{1} = 0, a_{2} = 4

Evaluate

(a - 4) (a^{4}) a^{2} \times 4

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

(a - 4) (a^{4}) a^{2} \times 4 = 0

Calculate

(a - 4) a^{4} \times a^{2} \times 4 = 0

Multiply the terms

More Steps

Multiply the terms

(a - 4) a^{4} \times a^{2} \times 4

Multiply the terms with the same base by adding their exponents

(a - 4) a^{4 + 2} \times 4

Add the numbers

(a - 4) a^{6} \times 4

Use the commutative property to reorder the terms

(a - 4) \times 4 a^{6}

Multiply the terms

4 a^{6} (a - 4)

4 a^{6} (a - 4) = 0

Elimination the left coefficient

a^{6} (a - 4) = 0

Separate the equation into 2 possible cases

a^{6} = 0 a - 4 = 0

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

a = 0 a - 4 = 0

Solve the equation

More Steps

Evaluate

a - 4 = 0

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

a = 0 + 4

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

a = 4

a = 0 a = 4

Solution

a_{1} = 0, a_{2} = 4

Show Solution