Factor (a+3b)^2+b(a-9b)-7ab

${(a + 3 b)}^{2} + b (a - 9 b) - 7 a b$

Rewrite ${(a + 3 b)}^{2}$ as $(a + 3 b) (a + 3 b)$ .

$(a + 3 b) (a + 3 b) + b (a - 9 b) - 7 a b$

Expand $(a + 3 b) (a + 3 b)$ using the FOIL Method.

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Apply the distributive property.

$a (a + 3 b) + 3 b (a + 3 b) + b (a - 9 b) - 7 a b$

Apply the distributive property.

$a \cdot a + a (3 b) + 3 b (a + 3 b) + b (a - 9 b) - 7 a b$

Apply the distributive property.

$a \cdot a + a (3 b) + 3 b a + 3 b (3 b) + b (a - 9 b) - 7 a b$

Simplify and combine like terms.

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Simplify each term.

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Multiply $a$ by $a$ .

$a^{2} + a (3 b) + 3 b a + 3 b (3 b) + b (a - 9 b) - 7 a b$

Rewrite using the commutative property of multiplication.

$a^{2} + 3 a b + 3 b a + 3 b (3 b) + b (a - 9 b) - 7 a b$

Rewrite using the commutative property of multiplication.

$a^{2} + 3 a b + 3 b a + 3 \cdot 3 b \cdot b + b (a - 9 b) - 7 a b$

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

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Move $b$ .

$a^{2} + 3 a b + 3 b a + 3 \cdot 3 (b \cdot b) + b (a - 9 b) - 7 a b$

Multiply $b$ by $b$ .

$a^{2} + 3 a b + 3 b a + 3 \cdot 3 b^{2} + b (a - 9 b) - 7 a b$

Multiply $3$ by $3$ .

$a^{2} + 3 a b + 3 b a + 9 b^{2} + b (a - 9 b) - 7 a b$

Add $3 a b$ and $3 b a$ .

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Move $b$ .

$a^{2} + 3 a b + 3 a b + 9 b^{2} + b (a - 9 b) - 7 a b$

Add $3 a b$ and $3 a b$ .

$a^{2} + 6 a b + 9 b^{2} + b (a - 9 b) - 7 a b$

Apply the distributive property.

$a^{2} + 6 a b + 9 b^{2} + b a + b (- 9 b) - 7 a b$

Rewrite using the commutative property of multiplication.

$a^{2} + 6 a b + 9 b^{2} + b a - 9 b \cdot b - 7 a b$

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

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Move $b$ .

$a^{2} + 6 a b + 9 b^{2} + b a - 9 (b \cdot b) - 7 a b$

Multiply $b$ by $b$ .

$a^{2} + 6 a b + 9 b^{2} + b a - 9 b^{2} - 7 a b$

Add $6 a b$ and $b a$ .

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Reorder $b$ and $a$ .

$a^{2} + 9 b^{2} + 6 a b + a b - 9 b^{2} - 7 a b$

Add $6 a b$ and $a b$ .

$a^{2} + 9 b^{2} + 7 a b - 9 b^{2} - 7 a b$

Subtract $9 b^{2}$ from $9 b^{2}$ .

$a^{2} + 7 a b + 0 - 7 a b$

Add $a^{2}$ and $0$ .

$a^{2} + 7 a b - 7 a b$

Subtract $7 a b$ from $7 a b$ .

$a^{2} + 0$

Add $a^{2}$ and $0$ .

$a^{2}$

Factor (a+3b)^2+b(a-9b)-7ab

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