Algebra Examples

$a^{2} (8 a + 9) - 10 (8 a + 9)$

Step 1

Apply the distributive property.

$a^{2} (8 a) + a^{2} \cdot 9 - 10 (8 a + 9)$

Step 2

Rewrite using the commutative property of multiplication.

$8 a^{2} a + a^{2} \cdot 9 - 10 (8 a + 9)$

Step 3

Move $9$ to the left of $a^{2}$ .

$8 a^{2} a + 9 \cdot a^{2} - 10 (8 a + 9)$

Step 4

Multiply $a^{2}$ by $a$ by adding the exponents.

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Step 4.1

Move $a$ .

$8 (a \cdot a^{2}) + 9 \cdot a^{2} - 10 (8 a + 9)$

Step 4.2

Multiply $a$ by $a^{2}$ .

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Step 4.2.1

Raise $a$ to the power of $1$ .

$8 (a^{1} a^{2}) + 9 \cdot a^{2} - 10 (8 a + 9)$

Step 4.2.2

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

$8 a^{1 + 2} + 9 \cdot a^{2} - 10 (8 a + 9)$

Step 4.3

Add $1$ and $2$ .

$8 a^{3} + 9 \cdot a^{2} - 10 (8 a + 9)$

$8 a^{3} + 9 a^{2} - 10 (8 a + 9)$

Step 5

Apply the distributive property.

$8 a^{3} + 9 a^{2} - 10 (8 a) - 10 \cdot 9$

Step 6

Multiply $8$ by $- 10$ .

$8 a^{3} + 9 a^{2} - 80 a - 10 \cdot 9$

Step 7

Multiply $- 10$ by $9$ .

$8 a^{3} + 9 a^{2} - 80 a - 90$