Algebra Examples

$4 b (2 a^{2} - 5 (3 a b - 2 b^{2})) + 29 a b^{2}$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 b (2 a^{2} - 5 (3 a b) - 5 (- 2 b^{2})) + 29 a b^{2}$

Step 1.1.2

Multiply $3$ by $- 5$ .

$4 b (2 a^{2} - 15 (a b) - 5 (- 2 b^{2})) + 29 a b^{2}$

Step 1.1.3

Multiply $- 2$ by $- 5$ .

$4 b (2 a^{2} - 15 a b + 10 b^{2}) + 29 a b^{2}$

Step 1.2

Apply the distributive property.

$4 b (2 a^{2}) + 4 b (- 15 a b) + 4 b (10 b^{2}) + 29 a b^{2}$

Step 1.3

Simplify.

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Step 1.3.1

Rewrite using the commutative property of multiplication.

$4 \cdot 2 b a^{2} + 4 b (- 15 a b) + 4 b (10 b^{2}) + 29 a b^{2}$

Step 1.3.2

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

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Step 1.3.2.1

Move $b$ .

$4 \cdot 2 b a^{2} + 4 (b \cdot b) (- 15 a) + 4 b (10 b^{2}) + 29 a b^{2}$

Step 1.3.2.2

Multiply $b$ by $b$ .

$4 \cdot 2 b a^{2} + 4 b^{2} (- 15 a) + 4 b (10 b^{2}) + 29 a b^{2}$

Step 1.3.3

Rewrite using the commutative property of multiplication.

$4 \cdot 2 b a^{2} + 4 b^{2} (- 15 a) + 4 \cdot 10 b \cdot b^{2} + 29 a b^{2}$

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $4$ by $2$ .

$8 b a^{2} + 4 b^{2} (- 15 a) + 4 \cdot 10 b \cdot b^{2} + 29 a b^{2}$

Step 1.4.2

Rewrite using the commutative property of multiplication.

$8 b a^{2} + 4 \cdot - 15 b^{2} a + 4 \cdot 10 b \cdot b^{2} + 29 a b^{2}$

Step 1.4.3

Multiply $4$ by $- 15$ .

$8 b a^{2} - 60 b^{2} a + 4 \cdot 10 b \cdot b^{2} + 29 a b^{2}$

Step 1.4.4

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

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Step 1.4.4.1

Move $b^{2}$ .

$8 b a^{2} - 60 b^{2} a + 4 \cdot 10 (b^{2} b) + 29 a b^{2}$

Step 1.4.4.2

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

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Step 1.4.4.2.1

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

$8 b a^{2} - 60 b^{2} a + 4 \cdot 10 (b^{2} b^{1}) + 29 a b^{2}$

Step 1.4.4.2.2

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

$8 b a^{2} - 60 b^{2} a + 4 \cdot 10 b^{2 + 1} + 29 a b^{2}$

Step 1.4.4.3

Add $2$ and $1$ .

$8 b a^{2} - 60 b^{2} a + 4 \cdot 10 b^{3} + 29 a b^{2}$

Step 1.4.5

Multiply $4$ by $10$ .

$8 b a^{2} - 60 b^{2} a + 40 b^{3} + 29 a b^{2}$

Step 2

Add $- 60 b^{2} a$ and $29 a b^{2}$ .

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Step 2.1

Move $b^{2}$ .

$8 b a^{2} + 40 b^{3} - 60 a b^{2} + 29 a b^{2}$

Step 2.2

Add $- 60 a b^{2}$ and $29 a b^{2}$ .

$8 b a^{2} + 40 b^{3} - 31 a b^{2}$

Step 3

Move $b$ .

$8 a^{2} b + 40 b^{3} - 31 a b^{2}$

Step 4

Move $40 b^{3}$ .

$8 a^{2} b - 31 a b^{2} + 40 b^{3}$