Basic Math Examples

$(w + 7 v - 5) (5 w - 6 v)$

Step 1

Expand $(w + 7 v - 5) (5 w - 6 v)$ by multiplying each term in the first expression by each term in the second expression.

$w (5 w) + w (- 6 v) + 7 v (5 w) + 7 v (- 6 v) - 5 (5 w) - 5 (- 6 v)$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$5 w \cdot w + w (- 6 v) + 7 v (5 w) + 7 v (- 6 v) - 5 (5 w) - 5 (- 6 v)$

Step 2.2

Multiply $w$ by $w$ by adding the exponents.

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Step 2.2.1

Move $w$ .

$5 (w \cdot w) + w (- 6 v) + 7 v (5 w) + 7 v (- 6 v) - 5 (5 w) - 5 (- 6 v)$

Step 2.2.2

Multiply $w$ by $w$ .

$5 w^{2} + w (- 6 v) + 7 v (5 w) + 7 v (- 6 v) - 5 (5 w) - 5 (- 6 v)$

Step 2.3

Rewrite using the commutative property of multiplication.

$5 w^{2} - 6 w v + 7 v (5 w) + 7 v (- 6 v) - 5 (5 w) - 5 (- 6 v)$

Step 2.4

Rewrite using the commutative property of multiplication.

$5 w^{2} - 6 w v + 7 \cdot 5 v w + 7 v (- 6 v) - 5 (5 w) - 5 (- 6 v)$

Step 2.5

Multiply $7$ by $5$ .

$5 w^{2} - 6 w v + 35 v w + 7 v (- 6 v) - 5 (5 w) - 5 (- 6 v)$

Step 2.6

Rewrite using the commutative property of multiplication.

$5 w^{2} - 6 w v + 35 v w + 7 \cdot - 6 v \cdot v - 5 (5 w) - 5 (- 6 v)$

Step 2.7

Multiply $v$ by $v$ by adding the exponents.

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Step 2.7.1

Move $v$ .

$5 w^{2} - 6 w v + 35 v w + 7 \cdot - 6 (v \cdot v) - 5 (5 w) - 5 (- 6 v)$

Step 2.7.2

Multiply $v$ by $v$ .

$5 w^{2} - 6 w v + 35 v w + 7 \cdot - 6 v^{2} - 5 (5 w) - 5 (- 6 v)$

Step 2.8

Multiply $7$ by $- 6$ .

$5 w^{2} - 6 w v + 35 v w - 42 v^{2} - 5 (5 w) - 5 (- 6 v)$

Step 2.9

Multiply $5$ by $- 5$ .

$5 w^{2} - 6 w v + 35 v w - 42 v^{2} - 25 w - 5 (- 6 v)$

Step 2.10

Multiply $- 6$ by $- 5$ .

$5 w^{2} - 6 w v + 35 v w - 42 v^{2} - 25 w + 30 v$

Step 3

Add $- 6 w v$ and $35 v w$ .

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Step 3.1

Move $w$ .

$5 w^{2} - 6 v w + 35 v w - 42 v^{2} - 25 w + 30 v$

Step 3.2

Add $- 6 v w$ and $35 v w$ .

$5 w^{2} + 29 v w - 42 v^{2} - 25 w + 30 v$

Step 4

Move $- 25 w$ .

$5 w^{2} + 29 v w - 42 v^{2} + 30 v - 25 w$

Step 5

Move $5 w^{2}$ .

$29 v w - 42 v^{2} + 5 w^{2} + 30 v - 25 w$

Step 6

Reorder $29 v w$ and $- 42 v^{2}$ .

$- 42 v^{2} + 29 v w + 5 w^{2} + 30 v - 25 w$