Simplify a(a+9b)^2

$a {(a + 9 b)}^{2}$

Step 1

Rewrite ${(a + 9 b)}^{2}$ as $(a + 9 b) (a + 9 b)$ .

$a ((a + 9 b) (a + 9 b))$

Step 2

Expand $(a + 9 b) (a + 9 b)$ using the FOIL Method.

Apply the distributive property.

$a (a (a + 9 b) + 9 b (a + 9 b))$

Apply the distributive property.

$a (a \cdot a + a (9 b) + 9 b (a + 9 b))$

Apply the distributive property.

$a (a \cdot a + a (9 b) + 9 b a + 9 b (9 b))$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

$a (a^{2} + a (9 b) + 9 b a + 9 b (9 b))$

Rewrite using the commutative property of multiplication.

$a (a^{2} + 9 a b + 9 b a + 9 b (9 b))$

Rewrite using the commutative property of multiplication.

$a (a^{2} + 9 a b + 9 b a + 9 \cdot 9 b \cdot b)$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$a (a^{2} + 9 a b + 9 b a + 9 \cdot 9 (b \cdot b))$

Multiply $b$ by $b$ .

$a (a^{2} + 9 a b + 9 b a + 9 \cdot 9 b^{2})$

Multiply $9$ by $9$ .

$a (a^{2} + 9 a b + 9 b a + 81 b^{2})$

Add $9 a b$ and $9 b a$ .

Move $b$ .

$a (a^{2} + 9 a b + 9 a b + 81 b^{2})$

Add $9 a b$ and $9 a b$ .

$a (a^{2} + 18 a b + 81 b^{2})$

Step 4

Apply the distributive property.

$a \cdot a^{2} + a (18 a b) + a (81 b^{2})$

Step 5

Simplify.

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

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

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

$a^{1} a^{2} + a (18 a b) + a (81 b^{2})$

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

$a^{1 + 2} + a (18 a b) + a (81 b^{2})$

Add $1$ and $2$ .

$a^{3} + a (18 a b) + a (81 b^{2})$

Rewrite using the commutative property of multiplication.

$a^{3} + 18 a (a b) + a (81 b^{2})$

Rewrite using the commutative property of multiplication.

$a^{3} + 18 a (a b) + 81 a b^{2}$

Step 6

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

Move $a$ .

$a^{3} + 18 (a \cdot a) b + 81 a b^{2}$

Multiply $a$ by $a$ .

$a^{3} + 18 a^{2} b + 81 a b^{2}$

Simplify a(a+9b)^2

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