Algebra Examples

$(3 b - 2) (5 - 2 b) + 6 b^{2}$

Step 1

Simplify each term.

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Step 1.1

Expand $(3 b - 2) (5 - 2 b)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$3 b (5 - 2 b) - 2 (5 - 2 b) + 6 b^{2}$

Step 1.1.2

Apply the distributive property.

$3 b \cdot 5 + 3 b (- 2 b) - 2 (5 - 2 b) + 6 b^{2}$

Step 1.1.3

Apply the distributive property.

$3 b \cdot 5 + 3 b (- 2 b) - 2 \cdot 5 - 2 (- 2 b) + 6 b^{2}$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $5$ by $3$ .

$15 b + 3 b (- 2 b) - 2 \cdot 5 - 2 (- 2 b) + 6 b^{2}$

Step 1.2.1.2

Rewrite using the commutative property of multiplication.

$15 b + 3 \cdot - 2 b \cdot b - 2 \cdot 5 - 2 (- 2 b) + 6 b^{2}$

Step 1.2.1.3

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

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Step 1.2.1.3.1

Move $b$ .

$15 b + 3 \cdot - 2 (b \cdot b) - 2 \cdot 5 - 2 (- 2 b) + 6 b^{2}$

Step 1.2.1.3.2

Multiply $b$ by $b$ .

$15 b + 3 \cdot - 2 b^{2} - 2 \cdot 5 - 2 (- 2 b) + 6 b^{2}$

Step 1.2.1.4

Multiply $3$ by $- 2$ .

$15 b - 6 b^{2} - 2 \cdot 5 - 2 (- 2 b) + 6 b^{2}$

Step 1.2.1.5

Multiply $- 2$ by $5$ .

$15 b - 6 b^{2} - 10 - 2 (- 2 b) + 6 b^{2}$

Step 1.2.1.6

Multiply $- 2$ by $- 2$ .

$15 b - 6 b^{2} - 10 + 4 b + 6 b^{2}$

Step 1.2.2

Add $15 b$ and $4 b$ .

$19 b - 6 b^{2} - 10 + 6 b^{2}$

Step 2

Combine the opposite terms in $19 b - 6 b^{2} - 10 + 6 b^{2}$ .

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Step 2.1

Add $- 6 b^{2}$ and $6 b^{2}$ .

$19 b + 0 - 10$

Step 2.2

Add $19 b$ and $0$ .

$19 b - 10$