Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

$(a + 3 b) (a + 3 b) - 3 b (2 a + 3 b)$

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

$a (a + 3 b) + 3 b (a + 3 b) - 3 b (2 a + 3 b)$

Step 1.2.2

Apply the distributive property.

$a \cdot a + a (3 b) + 3 b (a + 3 b) - 3 b (2 a + 3 b)$

Step 1.2.3

Apply the distributive property.

$a \cdot a + a (3 b) + 3 b a + 3 b (3 b) - 3 b (2 a + 3 b)$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $a$ by $a$ .

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

Step 1.3.1.2

Rewrite using the commutative property of multiplication.

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

Step 1.3.1.3

Rewrite using the commutative property of multiplication.

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

Step 1.3.1.4

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

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Step 1.3.1.4.1

Move $b$ .

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

Step 1.3.1.4.2

Multiply $b$ by $b$ .

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

Step 1.3.1.5

Multiply $3$ by $3$ .

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

Step 1.3.2

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

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Step 1.3.2.1

Move $b$ .

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

Step 1.3.2.2

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

$a^{2} + 6 a b + 9 b^{2} - 3 b (2 a + 3 b)$

Step 1.4

Apply the distributive property.

$a^{2} + 6 a b + 9 b^{2} - 3 b (2 a) - 3 b (3 b)$

Step 1.5

Rewrite using the commutative property of multiplication.

$a^{2} + 6 a b + 9 b^{2} - 3 \cdot 2 b a - 3 b (3 b)$

Step 1.6

Rewrite using the commutative property of multiplication.

$a^{2} + 6 a b + 9 b^{2} - 3 \cdot 2 b a - 3 \cdot 3 b \cdot b$

Step 1.7

Simplify each term.

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Step 1.7.1

Multiply $- 3$ by $2$ .

$a^{2} + 6 a b + 9 b^{2} - 6 b a - 3 \cdot 3 b \cdot b$

Step 1.7.2

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

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Step 1.7.2.1

Move $b$ .

$a^{2} + 6 a b + 9 b^{2} - 6 b a - 3 \cdot 3 (b \cdot b)$

Step 1.7.2.2

Multiply $b$ by $b$ .

$a^{2} + 6 a b + 9 b^{2} - 6 b a - 3 \cdot 3 b^{2}$

Step 1.7.3

Multiply $- 3$ by $3$ .

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

Step 2

Combine the opposite terms in $a^{2} + 6 a b + 9 b^{2} - 6 b a - 9 b^{2}$ .

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Step 2.1

Reorder the factors in the terms $6 a b$ and $- 6 b a$ .

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

Step 2.2

Subtract $6 a b$ from $6 a b$ .

$a^{2} + 9 b^{2} + 0 - 9 b^{2}$

Step 2.3

Add $a^{2} + 9 b^{2}$ and $0$ .

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

Step 2.4

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

$a^{2} + 0$

Step 2.5

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

$a^{2}$