Algebra Examples

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

Step 1

Expand $(a - b) (x^{2} - 5)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify each term.

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Step 2.1

Move $- 5$ to the left of $a$ .

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

Step 2.2

Multiply $- 5$ by $- 1$ .

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

Step 3

Expand $(b - a) (3 x + 5)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Apply the distributive property.

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

Step 4

Simplify each term.

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Step 4.1

Rewrite using the commutative property of multiplication.

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

Step 4.2

Move $5$ to the left of $b$ .

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

Step 4.3

Rewrite using the commutative property of multiplication.

$a x^{2} - 5 a - b x^{2} + 5 b + 3 b x + 5 b - 1 \cdot 3 a x - a \cdot 5$

Step 4.4

Multiply $- 1$ by $3$ .

$a x^{2} - 5 a - b x^{2} + 5 b + 3 b x + 5 b - 3 a x - a \cdot 5$

Step 4.5

Multiply $5$ by $- 1$ .

$a x^{2} - 5 a - b x^{2} + 5 b + 3 b x + 5 b - 3 a x - 5 a$

Step 5

Subtract $5 a$ from $- 5 a$ .

$a x^{2} - 10 a - b x^{2} + 5 b + 3 b x + 5 b - 3 a x$

Step 6

Add $5 b$ and $5 b$ .

$a x^{2} - 10 a - b x^{2} + 10 b + 3 b x - 3 a x$