Pre-Algebra Examples

$(5 - 2 a) (7 + 3 a)$

Step 1

Expand $(5 - 2 a) (7 + 3 a)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$5 (7 + 3 a) - 2 a (7 + 3 a)$

Step 1.2

Apply the distributive property.

$5 \cdot 7 + 5 (3 a) - 2 a (7 + 3 a)$

Step 1.3

Apply the distributive property.

$5 \cdot 7 + 5 (3 a) - 2 a \cdot 7 - 2 a (3 a)$

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 $5$ by $7$ .

$35 + 5 (3 a) - 2 a \cdot 7 - 2 a (3 a)$

Step 2.1.2

Multiply $3$ by $5$ .

$35 + 15 a - 2 a \cdot 7 - 2 a (3 a)$

Step 2.1.3

Multiply $7$ by $- 2$ .

$35 + 15 a - 14 a - 2 a (3 a)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$35 + 15 a - 14 a - 2 \cdot 3 a \cdot a$

Step 2.1.5

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

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Step 2.1.5.1

Move $a$ .

$35 + 15 a - 14 a - 2 \cdot 3 (a \cdot a)$

Step 2.1.5.2

Multiply $a$ by $a$ .

$35 + 15 a - 14 a - 2 \cdot 3 a^{2}$

Step 2.1.6

Multiply $- 2$ by $3$ .

$35 + 15 a - 14 a - 6 a^{2}$

Step 2.2

Subtract $14 a$ from $15 a$ .

$35 + a - 6 a^{2}$