Algebra Examples

$(3 e - 7 b) (8 e + 9 b)$

Step 1

Expand $(3 e - 7 b) (8 e + 9 b)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 e (8 e + 9 b) - 7 b (8 e + 9 b)$

Step 1.2

Apply the distributive property.

$3 e (8 e) + 3 e (9 b) - 7 b (8 e + 9 b)$

Step 1.3

Apply the distributive property.

$3 e (8 e) + 3 e (9 b) - 7 b (8 e) - 7 b (9 b)$

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 $3 e (8 e)$ .

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Step 2.1.1.1

Multiply $8$ by $3$ .

$24 e e + 3 e (9 b) - 7 b (8 e) - 7 b (9 b)$

Step 2.1.1.2

Raise $e$ to the power of $1$ .

$24 (e^{1} e) + 3 e (9 b) - 7 b (8 e) - 7 b (9 b)$

Step 2.1.1.3

Raise $e$ to the power of $1$ .

$24 (e^{1} e^{1}) + 3 e (9 b) - 7 b (8 e) - 7 b (9 b)$

Step 2.1.1.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$24 e^{1 + 1} + 3 e (9 b) - 7 b (8 e) - 7 b (9 b)$

Step 2.1.1.5

Add $1$ and $1$ .

$24 e^{2} + 3 e (9 b) - 7 b (8 e) - 7 b (9 b)$

Step 2.1.2

Multiply $9$ by $3$ .

$24 e^{2} + 27 e b - 7 b (8 e) - 7 b (9 b)$

Step 2.1.3

Multiply $8$ by $- 7$ .

$24 e^{2} + 27 e b - 56 b e - 7 b (9 b)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$24 e^{2} + 27 e b - 56 b e - 7 \cdot 9 b \cdot b$

Step 2.1.5

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

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Step 2.1.5.1

Move $b$ .

$24 e^{2} + 27 e b - 56 b e - 7 \cdot 9 (b \cdot b)$

Step 2.1.5.2

Multiply $b$ by $b$ .

$24 e^{2} + 27 e b - 56 b e - 7 \cdot 9 b^{2}$

Step 2.1.6

Multiply $- 7$ by $9$ .

$24 e^{2} + 27 e b - 56 b e - 63 b^{2}$

Step 2.2

Subtract $56 b e$ from $27 e b$ .

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Step 2.2.1

Move $e$ .

$24 e^{2} + 27 b e - 56 b e - 63 b^{2}$

Step 2.2.2

Subtract $56 b e$ from $27 b e$ .

$24 e^{2} - 29 b e - 63 b^{2}$

Step 3

Move $24 e^{2}$ .

$- 29 b e - 63 b^{2} + 24 e^{2}$

Step 4

Reorder $- 29 b e$ and $- 63 b^{2}$ .

$- 63 b^{2} - 29 b e + 24 e^{2}$