Precalculus Examples

$(b - 5) (2 b + 7)$

Step 1

Expand $(b - 5) (2 b + 7)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$b (2 b + 7) - 5 (2 b + 7)$

Step 1.2

Apply the distributive property.

$b (2 b) + b \cdot 7 - 5 (2 b + 7)$

Step 1.3

Apply the distributive property.

$b (2 b) + b \cdot 7 - 5 (2 b) - 5 \cdot 7$

$b (2 b) + b \cdot 7 - 5 (2 b) - 5 \cdot 7$

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

Rewrite using the commutative property of multiplication.

$2 b \cdot b + b \cdot 7 - 5 (2 b) - 5 \cdot 7$

Step 2.1.2

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

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Step 2.1.2.1

Move $b$ .

$2 (b \cdot b) + b \cdot 7 - 5 (2 b) - 5 \cdot 7$

Step 2.1.2.2

Multiply $b$ by $b$ .

$2 b^{2} + b \cdot 7 - 5 (2 b) - 5 \cdot 7$

$2 b^{2} + b \cdot 7 - 5 (2 b) - 5 \cdot 7$

Step 2.1.3

Move $7$ to the left of $b$ .

$2 b^{2} + 7 \cdot b - 5 (2 b) - 5 \cdot 7$

Step 2.1.4

Multiply $2$ by $- 5$ .

$2 b^{2} + 7 b - 10 b - 5 \cdot 7$

Step 2.1.5

Multiply $- 5$ by $7$ .

$2 b^{2} + 7 b - 10 b - 35$

$2 b^{2} + 7 b - 10 b - 35$

Step 2.2

Subtract $10 b$ from $7 b$ .

$2 b^{2} - 3 b - 35$

$2 b^{2} - 3 b - 35$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$