Algebra Examples

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

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

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

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Step 3.1.1.1

Move $a$ .

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

Step 3.1.1.2

Multiply $a$ by $a$ .

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

Step 3.1.2

Rewrite using the commutative property of multiplication.

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

Step 3.1.3

Multiply $5$ by $- 4$ .

$5 a^{2} - 20 a b + b a + b (- 4 b)$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$5 a^{2} - 20 a b + b a - 4 b \cdot b$

Step 3.1.5

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

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Step 3.1.5.1

Move $b$ .

$5 a^{2} - 20 a b + b a - 4 (b \cdot b)$

Step 3.1.5.2

Multiply $b$ by $b$ .

$5 a^{2} - 20 a b + b a - 4 b^{2}$

Step 3.2

Add $- 20 a b$ and $b a$ .

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Step 3.2.1

Reorder $b$ and $a$ .

$5 a^{2} - 20 a b + a b - 4 b^{2}$

Step 3.2.2

Add $- 20 a b$ and $a b$ .

$5 a^{2} - 19 a b - 4 b^{2}$