Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Rewrite using the commutative property of multiplication.

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

Step 3

Multiply $- 7$ by $3$ .

$3 \cdot 2 a x - 21 a + 5 b (7 - 2 x)$

Step 4

Multiply $3$ by $2$ .

$6 a x - 21 a + 5 b (7 - 2 x)$

Step 5

Apply the distributive property.

$6 a x - 21 a + 5 b \cdot 7 + 5 b (- 2 x)$

Step 6

Multiply $7$ by $5$ .

$6 a x - 21 a + 35 b + 5 b (- 2 x)$

Step 7

Rewrite using the commutative property of multiplication.

$6 a x - 21 a + 35 b + 5 \cdot - 2 b x$

Step 8

Multiply $5$ by $- 2$ .

$6 a x - 21 a + 35 b - 10 b x$

Step 9

Rewrite $6 a x - 21 a + 35 b - 10 b x$ in a factored form.

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Step 9.1

Reorder terms.

$- 21 a + 35 b + 6 a x - 10 b x$

Step 9.2

Factor out the greatest common factor from each group.

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Step 9.2.1

Group the first two terms and the last two terms.

$(- 21 a + 35 b) + 6 a x - 10 b x$

Step 9.2.2

Factor out the greatest common factor (GCF) from each group.

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

Step 9.3

Factor the polynomial by factoring out the greatest common factor, $- 3 a + 5 b$ .

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

Step 10

Factor $- 1$ out of $- 3 a + 5 b$ .

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Step 10.1

Factor $- 1$ out of $- 3 a$ .

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

Step 10.2

Factor $- 1$ out of $5 b$ .

$(- (3 a) - (- 5 b)) (7 - 2 x)$

Step 10.3

Factor $- 1$ out of $- (3 a) - (- 5 b)$ .

$- (3 a - 5 b) (7 - 2 x)$