Pre-Algebra Examples

$(a - b) (2 x^{2} + 9) - (b - a) (7 x - 6)$

Step 1

Simplify each term.

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Step 1.1

Expand $(a - b) (2 x^{2} + 9)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$a (2 x^{2} + 9) - b (2 x^{2} + 9) - (b - a) (7 x - 6)$

Step 1.1.2

Apply the distributive property.

$a (2 x^{2}) + a \cdot 9 - b (2 x^{2} + 9) - (b - a) (7 x - 6)$

Step 1.1.3

Apply the distributive property.

$a (2 x^{2}) + a \cdot 9 - b (2 x^{2}) - b \cdot 9 - (b - a) (7 x - 6)$

Step 1.2

Simplify each term.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$2 a x^{2} + a \cdot 9 - b (2 x^{2}) - b \cdot 9 - (b - a) (7 x - 6)$

Step 1.2.2

Move $9$ to the left of $a$ .

$2 a x^{2} + 9 \cdot a - b (2 x^{2}) - b \cdot 9 - (b - a) (7 x - 6)$

Step 1.2.3

Rewrite using the commutative property of multiplication.

$2 a x^{2} + 9 a - 1 \cdot 2 b x^{2} - b \cdot 9 - (b - a) (7 x - 6)$

Step 1.2.4

Multiply $- 1$ by $2$ .

$2 a x^{2} + 9 a - 2 b x^{2} - b \cdot 9 - (b - a) (7 x - 6)$

Step 1.2.5

Multiply $9$ by $- 1$ .

$2 a x^{2} + 9 a - 2 b x^{2} - 9 b - (b - a) (7 x - 6)$

Step 1.3

Apply the distributive property.

$2 a x^{2} + 9 a - 2 b x^{2} - 9 b + (- b - - a) (7 x - 6)$

Step 1.4

Multiply $- - a$ .

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Step 1.4.1

Multiply $- 1$ by $- 1$ .

$2 a x^{2} + 9 a - 2 b x^{2} - 9 b + (- b + 1 a) (7 x - 6)$

Step 1.4.2

Multiply $a$ by $1$ .

$2 a x^{2} + 9 a - 2 b x^{2} - 9 b + (- b + a) (7 x - 6)$

Step 1.5

Expand $(- b + a) (7 x - 6)$ using the FOIL Method.

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Step 1.5.1

Apply the distributive property.

$2 a x^{2} + 9 a - 2 b x^{2} - 9 b - b (7 x - 6) + a (7 x - 6)$

Step 1.5.2

Apply the distributive property.

$2 a x^{2} + 9 a - 2 b x^{2} - 9 b - b (7 x) - b \cdot - 6 + a (7 x - 6)$

Step 1.5.3

Apply the distributive property.

$2 a x^{2} + 9 a - 2 b x^{2} - 9 b - b (7 x) - b \cdot - 6 + a (7 x) + a \cdot - 6$

Step 1.6

Simplify each term.

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Step 1.6.1

Rewrite using the commutative property of multiplication.

$2 a x^{2} + 9 a - 2 b x^{2} - 9 b - 1 \cdot 7 b x - b \cdot - 6 + a (7 x) + a \cdot - 6$

Step 1.6.2

Multiply $- 1$ by $7$ .

$2 a x^{2} + 9 a - 2 b x^{2} - 9 b - 7 b x - b \cdot - 6 + a (7 x) + a \cdot - 6$

Step 1.6.3

Multiply $- 6$ by $- 1$ .

$2 a x^{2} + 9 a - 2 b x^{2} - 9 b - 7 b x + 6 b + a (7 x) + a \cdot - 6$

Step 1.6.4

Rewrite using the commutative property of multiplication.

$2 a x^{2} + 9 a - 2 b x^{2} - 9 b - 7 b x + 6 b + 7 a x + a \cdot - 6$

Step 1.6.5

Move $- 6$ to the left of $a$ .

$2 a x^{2} + 9 a - 2 b x^{2} - 9 b - 7 b x + 6 b + 7 a x - 6 a$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $6 a$ from $9 a$ .

$2 a x^{2} + 3 a - 2 b x^{2} - 9 b - 7 b x + 6 b + 7 a x$

Step 2.2

Add $- 9 b$ and $6 b$ .

$2 a x^{2} + 3 a - 2 b x^{2} - 3 b - 7 b x + 7 a x$

Step 2.3

Reorder.

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Step 2.3.1

Move $- 3 b$ .

$2 a x^{2} + 3 a - 2 b x^{2} - 7 b x + 7 a x - 3 b$

Step 2.3.2

Move $3 a$ .

$2 a x^{2} - 2 b x^{2} - 7 b x + 7 a x + 3 a - 3 b$

Step 2.3.3

Move $- 7 b x$ .

$2 a x^{2} - 2 b x^{2} + 7 a x - 7 b x + 3 a - 3 b$