Algebra Examples

$(2 a + 5 b) (a - 4 b)$

Step 1

Expand $(2 a + 5 b) (a - 4 b)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$2 a (a - 4 b) + 5 b (a - 4 b)$

Step 1.2

Apply the distributive property.

$2 a \cdot a + 2 a (- 4 b) + 5 b (a - 4 b)$

Step 1.3

Apply the distributive property.

$2 a \cdot a + 2 a (- 4 b) + 5 b a + 5 b (- 4 b)$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Move $a$ .

$2 (a \cdot a) + 2 a (- 4 b) + 5 b a + 5 b (- 4 b)$

Step 2.1.1.2

Multiply $a$ by $a$ .

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

Step 2.1.2

Rewrite using the commutative property of multiplication.

$2 a^{2} + 2 \cdot - 4 a b + 5 b a + 5 b (- 4 b)$

Step 2.1.3

Multiply $2$ by $- 4$ .

$2 a^{2} - 8 a b + 5 b a + 5 b (- 4 b)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$2 a^{2} - 8 a b + 5 b a + 5 \cdot - 4 b \cdot b$

Step 2.1.5

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

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Step 2.1.5.1

Move $b$ .

$2 a^{2} - 8 a b + 5 b a + 5 \cdot - 4 (b \cdot b)$

Step 2.1.5.2

Multiply $b$ by $b$ .

$2 a^{2} - 8 a b + 5 b a + 5 \cdot - 4 b^{2}$

Step 2.1.6

Multiply $5$ by $- 4$ .

$2 a^{2} - 8 a b + 5 b a - 20 b^{2}$

Step 2.2

Add $- 8 a b$ and $5 b a$ .

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Step 2.2.1

Move $b$ .

$2 a^{2} - 8 a b + 5 a b - 20 b^{2}$

Step 2.2.2

Add $- 8 a b$ and $5 a b$ .

$2 a^{2} - 3 a b - 20 b^{2}$