Algebra Examples

$(7 x - 8) (3 x + 5 y)$

Step 1

Expand $(7 x - 8) (3 x + 5 y)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 x (3 x + 5 y) - 8 (3 x + 5 y)$

Step 1.2

Apply the distributive property.

$7 x (3 x) + 7 x (5 y) - 8 (3 x + 5 y)$

Step 1.3

Apply the distributive property.

$7 x (3 x) + 7 x (5 y) - 8 (3 x) - 8 (5 y)$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$7 \cdot 3 x \cdot x + 7 x (5 y) - 8 (3 x) - 8 (5 y)$

Step 2.2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.2.1

Move $x$ .

$7 \cdot 3 (x \cdot x) + 7 x (5 y) - 8 (3 x) - 8 (5 y)$

Step 2.2.2

Multiply $x$ by $x$ .

$7 \cdot 3 x^{2} + 7 x (5 y) - 8 (3 x) - 8 (5 y)$

Step 2.3

Multiply $7$ by $3$ .

$21 x^{2} + 7 x (5 y) - 8 (3 x) - 8 (5 y)$

Step 2.4

Rewrite using the commutative property of multiplication.

$21 x^{2} + 7 \cdot 5 x y - 8 (3 x) - 8 (5 y)$

Step 2.5

Multiply $7$ by $5$ .

$21 x^{2} + 35 x y - 8 (3 x) - 8 (5 y)$

Step 2.6

Multiply $3$ by $- 8$ .

$21 x^{2} + 35 x y - 24 x - 8 (5 y)$

Step 2.7

Multiply $5$ by $- 8$ .

$21 x^{2} + 35 x y - 24 x - 40 y$