Pre-Algebra Examples

$- 4 a x^{7} (- 7 a x^{6} - 6 x^{3})$

Step 1

Apply the distributive property.

$- 4 a x^{7} (- 7 a x^{6}) - 4 a x^{7} (- 6 x^{3})$

Step 2

Multiply $a$ by $a$ by adding the exponents.

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Step 2.1

Move $a$ .

$- 4 (a \cdot a) x^{7} (- 7 x^{6}) - 4 a x^{7} (- 6 x^{3})$

Step 2.2

Multiply $a$ by $a$ .

$- 4 a^{2} x^{7} (- 7 x^{6}) - 4 a x^{7} (- 6 x^{3})$

Step 3

Multiply $x^{7}$ by $x^{3}$ by adding the exponents.

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Step 3.1

Move $x^{3}$ .

$- 4 a^{2} x^{7} (- 7 x^{6}) - 4 a (x^{3} x^{7}) \cdot - 6$

Step 3.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 4 a^{2} x^{7} (- 7 x^{6}) - 4 a x^{3 + 7} \cdot - 6$

Step 3.3

Add $3$ and $7$ .

$- 4 a^{2} x^{7} (- 7 x^{6}) - 4 a x^{10} \cdot - 6$

Step 4

Simplify each term.

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Step 4.1

Multiply $x^{7}$ by $x^{6}$ by adding the exponents.

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Step 4.1.1

Move $x^{6}$ .

$- 4 a^{2} (x^{6} x^{7}) \cdot - 7 - 4 a x^{10} \cdot - 6$

Step 4.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 4 a^{2} x^{6 + 7} \cdot - 7 - 4 a x^{10} \cdot - 6$

Step 4.1.3

Add $6$ and $7$ .

$- 4 a^{2} x^{13} \cdot - 7 - 4 a x^{10} \cdot - 6$

Step 4.2

Multiply $- 7$ by $- 4$ .

$28 a^{2} x^{13} - 4 a x^{10} \cdot - 6$

Step 4.3

Multiply $- 6$ by $- 4$ .

$28 a^{2} x^{13} + 24 a x^{10}$