Basic Math Examples

$(7 y - 6 u - 4) (5 y - 6 u)$

Step 1

Expand $(7 y - 6 u - 4) (5 y - 6 u)$ by multiplying each term in the first expression by each term in the second expression.

$7 y (5 y) + 7 y (- 6 u) - 6 u (5 y) - 6 u (- 6 u) - 4 (5 y) - 4 (- 6 u)$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$7 \cdot 5 y \cdot y + 7 y (- 6 u) - 6 u (5 y) - 6 u (- 6 u) - 4 (5 y) - 4 (- 6 u)$

Step 2.2

Multiply $y$ by $y$ by adding the exponents.

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Step 2.2.1

Move $y$ .

$7 \cdot 5 (y \cdot y) + 7 y (- 6 u) - 6 u (5 y) - 6 u (- 6 u) - 4 (5 y) - 4 (- 6 u)$

Step 2.2.2

Multiply $y$ by $y$ .

$7 \cdot 5 y^{2} + 7 y (- 6 u) - 6 u (5 y) - 6 u (- 6 u) - 4 (5 y) - 4 (- 6 u)$

Step 2.3

Multiply $7$ by $5$ .

$35 y^{2} + 7 y (- 6 u) - 6 u (5 y) - 6 u (- 6 u) - 4 (5 y) - 4 (- 6 u)$

Step 2.4

Rewrite using the commutative property of multiplication.

$35 y^{2} + 7 \cdot - 6 y u - 6 u (5 y) - 6 u (- 6 u) - 4 (5 y) - 4 (- 6 u)$

Step 2.5

Multiply $7$ by $- 6$ .

$35 y^{2} - 42 y u - 6 u (5 y) - 6 u (- 6 u) - 4 (5 y) - 4 (- 6 u)$

Step 2.6

Rewrite using the commutative property of multiplication.

$35 y^{2} - 42 y u - 6 \cdot 5 u y - 6 u (- 6 u) - 4 (5 y) - 4 (- 6 u)$

Step 2.7

Multiply $- 6$ by $5$ .

$35 y^{2} - 42 y u - 30 u y - 6 u (- 6 u) - 4 (5 y) - 4 (- 6 u)$

Step 2.8

Rewrite using the commutative property of multiplication.

$35 y^{2} - 42 y u - 30 u y - 6 \cdot - 6 u \cdot u - 4 (5 y) - 4 (- 6 u)$

Step 2.9

Multiply $u$ by $u$ by adding the exponents.

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Step 2.9.1

Move $u$ .

$35 y^{2} - 42 y u - 30 u y - 6 \cdot - 6 (u \cdot u) - 4 (5 y) - 4 (- 6 u)$

Step 2.9.2

Multiply $u$ by $u$ .

$35 y^{2} - 42 y u - 30 u y - 6 \cdot - 6 u^{2} - 4 (5 y) - 4 (- 6 u)$

Step 2.10

Multiply $- 6$ by $- 6$ .

$35 y^{2} - 42 y u - 30 u y + 36 u^{2} - 4 (5 y) - 4 (- 6 u)$

Step 2.11

Multiply $5$ by $- 4$ .

$35 y^{2} - 42 y u - 30 u y + 36 u^{2} - 20 y - 4 (- 6 u)$

Step 2.12

Multiply $- 6$ by $- 4$ .

$35 y^{2} - 42 y u - 30 u y + 36 u^{2} - 20 y + 24 u$

Step 3

Subtract $30 u y$ from $- 42 y u$ .

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Step 3.1

Move $y$ .

$35 y^{2} - 42 u y - 30 u y + 36 u^{2} - 20 y + 24 u$

Step 3.2

Subtract $30 u y$ from $- 42 u y$ .

$35 y^{2} - 72 u y + 36 u^{2} - 20 y + 24 u$

Step 4

Move $- 20 y$ .

$35 y^{2} - 72 u y + 36 u^{2} + 24 u - 20 y$

Step 5

Move $35 y^{2}$ .

$- 72 u y + 36 u^{2} + 35 y^{2} + 24 u - 20 y$

Step 6

Reorder $- 72 u y$ and $36 u^{2}$ .

$36 u^{2} - 72 u y + 35 y^{2} + 24 u - 20 y$