Basic Math Examples

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

Step 1

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

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

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2

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

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Step 2.2.1

Move $u$ .

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

Step 2.2.2

Multiply $u$ by $u$ .

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

Step 2.3

Multiply $4$ by $4$ .

$16 u^{2} + 4 u (7 y) - 5 y (4 u) - 5 y (7 y) - 4 (4 u) - 4 (7 y)$

Step 2.4

Rewrite using the commutative property of multiplication.

$16 u^{2} + 4 \cdot 7 u y - 5 y (4 u) - 5 y (7 y) - 4 (4 u) - 4 (7 y)$

Step 2.5

Multiply $4$ by $7$ .

$16 u^{2} + 28 u y - 5 y (4 u) - 5 y (7 y) - 4 (4 u) - 4 (7 y)$

Step 2.6

Rewrite using the commutative property of multiplication.

$16 u^{2} + 28 u y - 5 \cdot 4 y u - 5 y (7 y) - 4 (4 u) - 4 (7 y)$

Step 2.7

Multiply $- 5$ by $4$ .

$16 u^{2} + 28 u y - 20 y u - 5 y (7 y) - 4 (4 u) - 4 (7 y)$

Step 2.8

Rewrite using the commutative property of multiplication.

$16 u^{2} + 28 u y - 20 y u - 5 \cdot 7 y \cdot y - 4 (4 u) - 4 (7 y)$

Step 2.9

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

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Step 2.9.1

Move $y$ .

$16 u^{2} + 28 u y - 20 y u - 5 \cdot 7 (y \cdot y) - 4 (4 u) - 4 (7 y)$

Step 2.9.2

Multiply $y$ by $y$ .

$16 u^{2} + 28 u y - 20 y u - 5 \cdot 7 y^{2} - 4 (4 u) - 4 (7 y)$

Step 2.10

Multiply $- 5$ by $7$ .

$16 u^{2} + 28 u y - 20 y u - 35 y^{2} - 4 (4 u) - 4 (7 y)$

Step 2.11

Multiply $4$ by $- 4$ .

$16 u^{2} + 28 u y - 20 y u - 35 y^{2} - 16 u - 4 (7 y)$

Step 2.12

Multiply $7$ by $- 4$ .

$16 u^{2} + 28 u y - 20 y u - 35 y^{2} - 16 u - 28 y$

Step 3

Subtract $20 y u$ from $28 u y$ .

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Step 3.1

Move $y$ .

$16 u^{2} + 28 u y - 20 u y - 35 y^{2} - 16 u - 28 y$

Step 3.2

Subtract $20 u y$ from $28 u y$ .

$16 u^{2} + 8 u y - 35 y^{2} - 16 u - 28 y$